Linear and weakly nonlinear stability analysis of shallow mixing layers is presented in the doctoral thesis. The flow is assumed to be slightly curved along the longitudinal coordinate. The friction coefficient varies with respect to the transverse coordinate. Linear stability is analyzed from temporal and spatial points of view. The problem is generalized for the case of two-component shallow flows. Two approaches for weakly nonlinear stability are presented as well. It is shown that the amplitude equation is the complex Ginzburg-Landau equation (parallel flow assumption). A first-order amplitude evolution equation is derived (slow longitudinal variation of the base flow).