Abstract: The present invention relates to a rotary piston system mounted within an engine or a pump and characterized in that a piston moves inside a housing, thus reducing or enlarging closed spaces. The piston is an oloid element rotating about its axis. The internal space consists of two identical shells contiguously assembled along the equatorial planes thereof. The space defined by the shells inside the housing has an enveloping surface resulting from the biaxial rotation of the oloid element, the maximum diameter of which corresponds to its longitudinal profile.