Exhibit 10.1

AGREEMENT

This Agreement, dated as of June 4, 2007 (“Agreement”), is by and among CRYO-CELL International, Inc., a Delaware corporation (the “Company”), and the other persons and entities that are signatories hereto (collectively, the “Holders,” and each, individually, a “Holder”), each of whom is a holder of common shares, par value $.01, of the Company (the “Shares”).

WHEREAS, the Board of Directors of the Company (the “Board”), upon recommendation of the Governance Committee of the Board, has determined that it is in the best interests of the Company and its shareholders to nominate Andrew J. Filipowski for election as a director at the Company’s 2007 annual meeting of shareholders, provided that the Holders agree to certain limitations on their activities as described herein, and the Holders are willing to agree to such limitations.

NOW, THEREFORE, in consideration of the foregoing premises and the mutual covenants and agreements contained herein, and for other good and valuable consideration, the receipt and sufficiency of which is hereby acknowledged, the parties hereto, intending to be legally bound hereby, agree as follows:

1. Representations and Warranties of the Company. The Company hereby represents and warrants to the Holders that (i) this Agreement has been duly authorized, executed and delivered by the Company, and is a valid and binding obligation of the Company, enforceable against the Company in accordance with its terms, except as enforcement thereof may be limited by applicable bankruptcy, insolvency, reorganization, moratorium, fraudulent conveyance or similar laws generally affecting the rights of creditors and subject to general equity principles; and (ii) neither the execution of this Agreement nor the consummation of any of the transactions contemplated hereby nor the fulfillment of the terms hereof, in each case in accordance with the terms hereof, will conflict with, result in a breach or violation or imposition of any lien, charge or encumbrance upon any property or assets of the Company or any of its subsidiaries pursuant to the terms of any indenture, contract, lease, mortgage, deed of trust, note agreement, loan agreement or other agreement, obligation, condition, covenant or instrument to which the Company or any of its subsidiaries is a party or bound or to which its or their property is subject.

2. Representations and Warranties of the Holders. Each of the Holders represents and warrants to the Company that this Agreement has been duly authorized, executed and delivered by such member, and is a valid and binding obligation of such member, enforceable against such member in accordance with its terms, except as enforcement thereof may be limited by applicable bankruptcy, insolvency, reorganization, moratorium, fraudulent conveyance or similar laws generally affecting the rights of creditors and subject to general equity principles.

3. Board of Directors Matters.

(a) The Board will cause the size of the Board to be increased, effective as of the date of the 2007 annual meeting, so that it is comprised of six (6) directors. The Board, upon recommendation of the Governance Committee, agrees to nominate Andrew J. Filipowski as part of management’s slate of nominees for election to the Board at the 2007 annual meeting.

(b) Each of the Holders agrees to vote all of the Shares for which he or it has voting power, in favor of each member of management’s slate of nominees for election to the Board at the 2007 annual meeting, and not to subsequently change or revoke such vote or vote for any other nominees besides management’s slate at the 2007 annual meeting.

4. Standstill.

(a) Each of the Holders agrees that, from the date of this Agreement until the earlier of (i) the Company’s 2008 annual meeting of shareholders or (ii) such earlier time as Andrew J. Filipowski is no longer a director of the Company for a reason other than his voluntary resignation from the Board, without the prior written consent of the Board specifically expressed in a written resolution adopted by a majority vote of the entire Board, neither such Holder nor any of its Affiliates or Associates under its control or direction will, and it will cause each of its Affiliates and Associates under its control not to, directly or indirectly, in any manner: (A) engage in any solicitation of proxies or consents to vote any voting securities of the Company in opposition to the recommendations of the Board or become a participant in any election contest with respect to the Company; (B) otherwise take any action to obtain representation on the Board, except for actions permitted expressly by this Agreement; (C) take any action that is designed to require the Company to make a public announcement regarding its strategic alternatives; (D) enter into any agreements with any third party with respect to any of the foregoing; or (E) make any public announcement with respect to any of the foregoing, except as advised by counsel to comply with applicable law and regulations.

(b) As used in this Agreement, the terms “Affiliate” and “Associate” shall have the respective meanings set forth in Rule 12b-2 promulgated by the Securities and Exchange Commission (the “SEC”) under the Securities Exchange Act of 1934, as amended (the “Exchange Act”); the terms “beneficial owner” and “beneficial ownership” shall have the same meanings as set forth in Rule 13d-3 promulgated by the SEC under the Exchange Act; and the terms “person” or “persons” shall mean any individual, corporation (including not-for-profit), general or limited partnership, limited liability company, joint venture, estate, trust, association, organization or other entity of any kind or nature; and “group” shall have the meaning as set forth in Rule 13d-5 promulgated by the SEC under the Exchange Act.

5. Confidentiality. The Holders (each, a “Recipient”) each acknowledge the confidential and proprietary nature of the Confidential Information (as defined below) and agree that the Confidential Information (a) will be kept confidential by Recipient and Recipient’s Representatives and (b) will not be disclosed by Recipient (except to other Recipients and their Affiliates and Associates and such person’s Representatives to the extent contemplated by this Agreement) or by Recipient’s Representatives (as defined below) to any person except with the specific prior written consent of the Company or except as expressly otherwise permitted by this Agreement. It is understood that (x) Recipient may disclose Confidential Information only to those of Recipient’s Representatives who are informed by Recipient of the confidential nature of the Confidential Information and the obligations of this Agreement and (y) Recipient shall be responsible for the breach of the provisions of this Section 5 by Recipient’s Representatives. As used in this Agreement, the term “Confidential Information” means and includes any and all of

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the information concerning the business and affairs of the Company that may hereafter be disclosed to Recipient by the Company or by the directors, officers, employees, agents, consultants, advisors or other representatives, including legal counsel, accountants and financial advisors (“Representatives”) of the Company; provided that “Confidential Information” shall not include information that (a) was in or enters the public domain or was or becomes generally available to the public other than as a result of disclosure by Recipient or any Representative thereof, (b) was independently acquired by Recipient without violating any of the obligations of Recipient or its Representatives under this Agreement, or under any other contractual, legal, fiduciary or binding obligation of Recipient or its Representatives with or to the Company, (c) was available, or becomes available, to Recipient on a nonconfidential basis other than as a result of its disclosure to Recipient by the Company or any Representative of the Company, but only if to the knowledge of Recipient the source of such information is not bound by a confidentiality agreement with the Company or is not otherwise prohibited from transmitting the information to Recipient or Recipient’s Representatives by a contractual, legal, fiduciary or other binding obligation with or to the Company, or (d) was independently developed by Recipient or its Representatives without reference to any other Confidential Information.

6. Specific Performance. Each of the Holders, on the one hand, and the Company, on the other hand, acknowledges and agrees that irreparable injury to the other party hereto would occur in the event any of the provisions of this Agreement were not performed in accordance with their specific terms or were otherwise breached and that such injury would not be adequately compensable in damages. It is accordingly agreed that the Holders or any of them, on the one hand, and the Company, on the other hand (the “Moving Party”), shall each be entitled to specific enforcement of, and injunctive relief to prevent any violation of, the terms hereof, and the other party hereto will not take action, directly or indirectly, in opposition to the Moving Party seeking such relief on the grounds that any other remedy or relief is available at law or in equity.

7. Jurisdiction; Applicable Law. Each of the parties hereto (a) consents to submit itself to the personal jurisdiction of the federal or state courts of the State of Delaware in the event any dispute arises out of this Agreement or the transactions contemplated by this Agreement, (b) agrees that it shall not attempt to deny or defeat such personal jurisdiction by motion or other request for leave from any such court, (c) agrees that it shall not bring any action relating to this Agreement or the transactions contemplated by this Agreement in any court other than the federal or state courts of the State of Delaware, and each of the parties irrevocably waives the right to trial by jury and (d) each of the parties irrevocably consents to service of process by first class certified mail, return receipt requested, postage prepaid, to the address of such parties’ principal place of business or as otherwise provided by applicable law. THIS AGREEMENT SHALL BE GOVERNED IN ALL RESPECTS, INCLUDING VALIDITY, INTERPRETATION AND EFFECT, BY THE LAWS OF THE STATE OF DELAWARE APPLICABLE TO CONTRACTS EXECUTED AND TO BE PERFORMED WHOLLY WITHIN SUCH STATE WITHOUT GIVING EFFECT TO THE CHOICE OF LAW PRINCIPLES OF SUCH STATE.

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8. Representative. Each of the Holders hereby irrevocably appoints Andrew J. Filipowski as such member’s attorney-in-fact and representative (the “Representative”), in such member’s place and stead, to do any and all things and to execute any and all documents and give and receive any and all notices or instructions in connection with this Agreement and the transactions contemplated hereby. The Company shall be entitled to rely, as being binding on each of the Holders, upon any action taken by the Representative or upon any document, notice, instruction or other writing given or executed by the Representative.

9. Severability. If at any time subsequent to the date hereof, any provision of this Agreement shall be held by any court of competent jurisdiction to be illegal, void or unenforceable, such provision shall be of no force and effect, but the illegality or unenforceability of such provision shall have no effect upon the legality or enforceability of any other provision of this Agreement.

10. Counterparts. This Agreement may be executed in two or more counterparts which together shall constitute a single agreement.

11. Entire Agreement; Amendment. This Agreement contains the entire understanding of the parties hereto with respect to its subject matter. There are no restrictions, agreements, promises, representations, warranties, covenants or undertakings other than those expressly set forth herein. This Agreement may be amended only by a written instrument duly executed by the parties hereto, or in the case of the Holders, the Representative, or their respective successors or assigns.

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[Signature Page to Agreement]

IN WITNESS WHEREOF, this Agreement has been duly executed and delivered by the duly authorized signatories of the parties as of the date hereof.