The invention relates to a helico-axial pump (1) for pumping a multi-phase mixture (M), said helico-axial pump (1) including a rotor (2) rotatably journalled in a pump housing (6) about a longitudinal axis (A), wherein the rotor (2) includes a compression stage (K) with a helico-axial impeller (3) and a stator (4) for the compression of the multi-phase mixture (M). In accordance with the invention a hydrodynamic stabilization element (7, 71, 72, 73) having a stabilization surface (700) is provided in the pump housing (6) and designed such that a stabilization gap (8) is formed upstream of the stabilization medium, so that in the operating state a hydrodynamic stabilization layer (S) can be formed from a stabilization medium in the stabilization gap (S). The invention further relates to a rotor (2) for a helico-axial pump (1), a method for the hydrodynamic journaling of a rotor (2) of a helico-axial pump (1) as well as to a hybrid pump with a rotor (2) for a helico-axial pump 1.