The process of the invention comprises the implementation of axenic conditions, with use of a liquid single-phase culture medium. For obtaining the amastigote forms, this medium is buffered at a pH of 5.5 to 6.5 and has an osmolarity of at least 400 milliosmoles/kg of liquid, and in particular 400 to 550 milliosmoles/kg of liquid. For obtaining promastigote forms, this medium is buffered at a pH of 7 to 7.5 and has an osmolarity of at least 300 milliosmoles/kg of liquid. This process allows the adaptation and culture in vitro of different stages of tissular parasites, such as leishmanias and T. cruzi or also hematoprotozoa.