A Moineau pump or Moineau compressor includes a conically designed inner (4) and a conically designed outer (8) element, whose longitudinal axes (X1, X2) run at an angle to one another and intersect at a point. The pump or compressor has at least two sections (2a, 2b, 2c, 2d) in the axial direction. A part (4b) of the inner element (4) located in a second section (2b) is arranged rotated with respect to a part (4a) of the inner element located in a first section (2a) about the longitudinal axis (X1) of the inner element (4). A part (8b) of the outer element (8) located in the second section (2b) is arranged rotated with respect to an other part (8a) of the outer element (8) located in the first section (2a) about the longitudinal axis (X2) of the outer element (8).