The present invention relates to a process for animal, preferably human, diploid anchorage-dependent cell culture, in the absence of exogenous components of primary animal origin, and to a cell culture medium substantially free of exogenous components of primary animal origin suitable for carrying out said process. In particular the invention concerns a cell culture medium which comprises at least one, more preferably several, exogenous animal-free growth factors. The present invention also relates to a process for cultivating animal, preferably human diploid anchorage-dependent cells in a medium according to the invention, involving the use of a trypsin substitute of non-animal origin for passaging cells. The invention further relates to a process for producing viruses, viral vaccines and the like.