The present invention relates to a method and composition for the cryopreservation of adipose tissue with the intention to use this tissue in the culturing of stem and/or progenitor cells. The method uses a specific cryoprotection medium to prevent damage of the original tissue during the cryopreservation while still maintaining a high viability of the stem and/or progenitor cells obtained from the cryopreserved adipose tissue. Furthermore the cryoprotection medium of the present invention does not contain any kind of xenogeneic sera, a critical factor since it is the intention of that the cryopreserved tissue is used for obtaining stem and/or progenitor cells that can be used in medicine. The cryoprotection medium is characterized in that it is a solution of physiological water comprising glycerol and sucrose and/or trehalose and optionally serum albumin.