There are two well known theories to describe the motion and thermodynamics of superfluids when a large number of quantized vortex lines are present and when the phenomena under study are on scales large compared with the vortex line spacing. These works have been criticised on the grounds that their governing equations for the smoothly varying, spatially averaged, fields do not satisfy the accepted invariance principles basic to modern continuum mechanics. This paper demonstrates one way in which such theories can arise from a properly invariant continuum approach and indicates the presence of hitherto unconsidered terms that bring them closer to the generally accepted microscopic picture. The resulting theory has applications both to rotating helium II in the laboratory, and to rotating neutron stars (pulsars). © 1977 Springer-Verlag.