A conical screw compressor or pump comprising: an inner element configured to rotate around a first axis ; an outer element configured to rotate around a second axis ; and means for fixing a longitudinal position of the inner element along the first axis and that fixes a longitudinal position of the outer element along the second axis thereby fixing the inner element and the outer element in a relative longitudinal position during rotation; wherein an outer surface of the inner element and an inner surface of the outer element comprise cooperating grooves and teeth that intermesh on rotation; the first axis and the second axis are each stationary and the first axis is inclined relative to the second axis ; the conical screw compressor or pump further comprises a housing in which the inner and outer elements are positioned; the means for fixing the longitudinal positions of the inner and outer elements further comprise at least two bearings between the outer element and the housing, which at least two bearings between the outer element and the housing comprise a bearing proximate to a discharge end of the outer element and a further bearing proximate to a suction end of the outer element, characterized in that, the bearing and the further bearing are each located between the outer element and the housing so as to allow relative axial rotation of the outer element and the housing while restricting longitudinal motion of the outer element and the housing ; the inner element is coupled to a shaft and the means for fixing the longitudinal positions of the inner and outer elements further comprise at least one bearing between the shaft and the housing , the at least one bearing between the shaft and the housing being configured to allow relative axial rotation of the inner element and the housing while restricting relative longitudinal motion of the inner element and the housing . an inner element configured to rotate around a first axis ; an outer element configured to rotate around a second axis ; and means for fixing a longitudinal position of the inner element along the first axis and that fixes a longitudinal position of the outer element along the second axis thereby fixing the inner element and the outer element in a relative longitudinal position during rotation; wherein an outer surface of the inner element and an inner surface of the outer element comprise cooperating grooves and teeth that intermesh on rotation; the first axis and the second axis are each stationary and the first axis is inclined relative to the second axis ; the conical screw compressor or pump further comprises a housing in which the inner and outer elements are positioned; the means for fixing the longitudinal positions of the inner and outer elements further comprise at least two bearings between the outer element and the housing, which at least two bearings between the outer element and the housing comprise a bearing proximate to a discharge end of the outer element and a further bearing proximate to a suction end of the outer element, characterized in that, the bearing and the further bearing are each located between the outer element and the housing so as to allow relative axial rotation of the outer element and the housing while restricting longitudinal motion of the outer element and the housing ; the inner element is coupled to a shaft and the means for fixing the longitudinal positions of the inner and outer elements further comprise at least one bearing between the shaft and the housing , the at least one bearing between the shaft and the housing being configured to allow relative axial rotation of the inner element and the housing while restricting relative longitudinal motion of the inner element and the housing . <EOS>