Motor-pump unit for conveying a fluid, comprising a pump base (3; 3'), a first pump rotor which is rotatably mounted with respect to a first axis and is rotatably coupled to the rotor of an electric motor, the stator of which is fixed relative to the pump base (3; 3'), and a second pump rotor which is rotatable about a second axis which intersects the first axis at a non-zero angle at an axis intersection point, wherein - the two pump rotors (4, 5) have mutually meshing toothings (12, 15) with a number of teeth (13, 16) differing by one from one another in such a way that chambers enclosed between the two toothings (12, 15) increase or decrease in volume as the two pump rotors (4, 5) rotate about the respective axis (X, Y), - the first pump rotor has, radially outside the associated toothing, a collar with an inner wall which is spherical with respect to the axis intersection point and against which the second pump rotor bears with a corresponding, spherically shaped outer surface in such a way that the chambers are bounded radially on the outside by the spherical inner wall of the collar, - the second pump rotor has, radially inside the associated toothing, a dome-shaped region with an outer wall which is spherical with respect to the axis intersection point and against which the first pump rotor bears with a corresponding, spherically shaped inner surface in such a way that the chambers are bounded radially on the inside by the spherical outer wall of the dome-shaped region, characterized in that - the end face of the second pump rotor facing away from the associated toothing is designed as a sliding surface, by means of which the second pump rotor is supported on a support surface designed on the pump base (3; 3') perpendicular to the second axis, - the second pump rotor has a number of fluid openings corresponding to the number of teeth of its toothing, which open into a respective tooth space, and - two separate recesses (28, 29) are provided on the support surface, which communicate fluidically with different fluid connections (30, 31; 30', 31') on the motor-pump unit. - the two pump rotors (4, 5) have mutually meshing toothings (12, 15) with a number of teeth (13, 16) differing by one from one another in such a way that chambers enclosed between the two toothings (12, 15) increase or decrease in volume as the two pump rotors (4, 5) rotate about the respective axis (X, Y), - the first pump rotor has, radially outside the associated toothing, a collar with an inner wall which is spherical with respect to the axis intersection point and against which the second pump rotor bears with a corresponding, spherically shaped outer surface in such a way that the chambers are bounded radially on the outside by the spherical inner wall of the collar, - the second pump rotor has, radially inside the associated toothing, a dome-shaped region with an outer wall which is spherical with respect to the axis intersection point and against which the first pump rotor bears with a corresponding, spherically shaped inner surface in such a way that the chambers are bounded radially on the inside by the spherical outer wall of the dome-shaped region, - the end face of the second pump rotor facing away from the associated toothing is designed as a sliding surface, by means of which the second pump rotor is supported on a support surface designed on the pump base (3; 3') perpendicular to the second axis, - the second pump rotor has a number of fluid openings corresponding to the number of teeth of its toothing, which open into a respective tooth space, and - two separate recesses (28, 29) are provided on the support surface, which communicate fluidically with different fluid connections (30, 31; 30', 31') on the motor-pump unit.