In this Letter we construct a spinor transport theory and derive the equations of motion for the distribution functions for currents in noncollinear magnetic multilayers. We find the length scale which characterizes the transverse spin current is of the order of 3 nm for a ferromagnetic 3d transition metal such as Co; this alters one's prediction of the spin torque generated for free magnetic layers less than 3 nm. In the limit of large exchange splitting we reproduce the results previously found for spin currents across noncollinear multilayers inasmuch as there are no transverse spin currents in the layers themselves in this limit.