The invention relates to a rotary piston machine for compressible media, comprising rotary pistons that are sealed into a common housing and that rotate with one another in a forced manner. Said rotary pistons have a plurality of disc-type sections, which engage in pairs with one another and whose thickness and/or diameter reduces towards the pressure side. Each disc has an outer surface (M1, m1) and an inner surface (K1", k1"), respectively connected by an intermediate surface (Z1"), the sector angle of the outer surface and the inner surface of each disc being unequal. The discs have different transverse profile contours, which are periodically repeated along the piston axis and each disc is offset at an angle to the two neighbouring discs of the same piston in such a way that said three discs have a common surface section and form a chamber.