The flow of liquid helium II in a channel is considered both when the mean velocity of the superfluid component is zero and when that of the normal component is zero. Possible flow regimes and critical velocities are discussed and in both cases the magnitude and form of the mutual friction are calculated using a simple semi-classical approximation. The discussion is extended to the case of heat currents with no net mass flow and compared with experiment. The observation of two different critical velocities below about 1·6°K, but only one near the Λ-point, is accounted for. The observed mutual friction is found to be in reasonable agreement with the values calculated for high and low temperatures. In the Appendix it is shown that, below the Bose condensation temperature, an ideal Bose gas is a type-II superfluid with vanishing Ginzburg–Landau parameter. The angular-momentum defect of the rotating gas is calculated for use in the main paper.