This paper describes and further develops the understanding of toroidal momentum transport. Nonlinear gyro-kinetic simulations of the ion
temperature gradient mode with adiabatic electrons show a strong coupling between the momentum and ion heat transport, with the ratio of the transport coefficients close to 1. Linear theory using a global description predicts an off-diagonal contribution to the momentum flux even in the absence of a radial electric field. The influence of the toroidal velocity gradient on the ion temperature profile is found to be small in the H-mode. These predictions are in qualitative agreement with experimental observations.