Two sets of the balance equations for a compressible and non-Newtonian fluid in helical coordinate systems are developed. They are associated with two different ways of decomposing a velocity vector; one with three non-orthogonal velocity components in the normal, tangential and helical directions and the other with three orthogonal velocity components in the radial, cross-channel and down-channel directions. It is shown that that compared with classical rectangular and cylindrical coordinate systems, a helical coordinate system is most suitable for describing flow in a screw extruder, in which the flow path is characterised by two inherent geometrical features: curvature and helicity.