A method is disclosed for the in vitro growth and development of cells obtained from the follicles of a mammal to reproductively competent oocytes. By incubating these cells, which comprise small and medium oocytes, in a series of specific hormone-supplemented tissue culture media as described herein, they can be induced to grow and develop into reproductively competent oocytes. After a further maturation step in which chromosome number reduction occurs, the oocytes are fertilizable.