Hydraulic motor-pump unit with fixed or variable displacement, comprising: • at least one central motor-pump rotor which comprises a central rotor power take-off and which is housed on or in a motor-pump casing, the said rotor being able to rotate in at least one central rotor bearing that the said casing comprises while remaining in the most fluidtight possible contact with at least one inlet-outlet distributor kept approximately stationary with respect to the said casing, characterized in that the said distributor being able to connect at least one hydraulic cylinder formed radially or tangentially in the said rotor with at least one inlet-outlet internal duct and at least one inlet-outlet external duct via a central rotor inlet-outlet internal passage and a central rotor inlet-outlet orifice respectively, these being formed in the motor-pump central rotor, one of the ends of the said ducts (57, 58) being anchored directly or indirectly and in a fluidtight manner in the motor-pump casing while the other end of the said ducts (57, 58) is anchored in a fluidtight manner in the inlet-outlet distributor; and in that the hydraulic motor-pump unit with fixed or variable displacement comprises: • at least one hydraulic piston able to move translationally in the hydraulic cylinder and able to push a hydraulic piston guided tappet or being able to be pushed by the latter, the said tappet being guided in translation by a tappet guide formed radially or tangentially in the motor-pump central rotor; • at least one tangential arm of which one of the ends is articulated in the motor-pump central rotor while the other end comprises a tangentialarm-on-tappet bearing face which can exert a force on a tappet-on-tangential-arm line of action that the hydraulic piston guided tappet comprises, the direction of the said force being approximately tangential to the axis of rotation of the said arm; • at least one motor-pump peripheral rotor made up of at least one peripheral rotor cylindrical case of which one of the ends at least ends in a peripheral rotor flange, the said peripheral rotor being able to rotate in at least one peripheral rotor bearing borne by a peripheral rotor stator which is directly or indirectly secured to the motor-pump casing, the motor-pump central rotor being fully or partially housed inside the said peripheral rotor; • at least antifriction means that the tangential arm comprises on its face situated opposite to the tangential-arm-on-tappet bearing face, the said means bearing on the internal surface of the peripheral rotor cylindrical case. • at least one central motor-pump rotor which comprises a central rotor power take-off and which is housed on or in a motor-pump casing, the said rotor being able to rotate in at least one central rotor bearing that the said casing comprises while remaining in the most fluidtight possible contact with at least one inlet-outlet distributor kept approximately stationary with respect to the said casing, characterized in that the said distributor being able to connect at least one hydraulic cylinder formed radially or tangentially in the said rotor with at least one inlet-outlet internal duct and at least one inlet-outlet external duct via a central rotor inlet-outlet internal passage and a central rotor inlet-outlet orifice respectively, these being formed in the motor-pump central rotor, one of the ends of the said ducts (57, 58) being anchored directly or indirectly and in a fluidtight manner in the motor-pump casing while the other end of the said ducts (57, 58) is anchored in a fluidtight manner in the inlet-outlet distributor; • at least one hydraulic piston able to move translationally in the hydraulic cylinder and able to push a hydraulic piston guided tappet or being able to be pushed by the latter, the said tappet being guided in translation by a tappet guide formed radially or tangentially in the motor-pump central rotor; • at least one tangential arm of which one of the ends is articulated in the motor-pump central rotor while the other end comprises a tangentialarm-on-tappet bearing face which can exert a force on a tappet-on-tangential-arm line of action that the hydraulic piston guided tappet comprises, the direction of the said force being approximately tangential to the axis of rotation of the said arm; • at least one motor-pump peripheral rotor made up of at least one peripheral rotor cylindrical case of which one of the ends at least ends in a peripheral rotor flange, the said peripheral rotor being able to rotate in at least one peripheral rotor bearing borne by a peripheral rotor stator which is directly or indirectly secured to the motor-pump casing, the motor-pump central rotor being fully or partially housed inside the said peripheral rotor; • at least antifriction means that the tangential arm comprises on its face situated opposite to the tangential-arm-on-tappet bearing face, the said means bearing on the internal surface of the peripheral rotor cylindrical case.