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. Linear stability is analysed from temporal and spatial points of view under the rigid-lid assumption. The friction coefficient varies with respect to the transverse coordinate (the case of constant friction coefficient usually analysed in the literature is a particular case of the analysis presented in the Thesis). The corresponding linear stability problems are solved numerically using pseudospectral collocation method based on Chebyshev polynomials. In addition, the problem is generalized for the case of two-component shallow flows under the assumption of large Stokes numbers. The effect of asymmetry of base flow profile on the stability characteristics is analysed. Two approaches to weakly nonlinear stability are presented as well. The first approach is based on the parallel flow assumption and can be applied for the case where the bed-friction number is slightly smaller than the critical value. Using the method of multiple scales, an amplitude evolution equation is derived for the most unstable mode. It is shown that for slightly curved shallow mixing layers, which contain or do not contain particles, the amplitude equation is the complex Ginzburg-Landau equation. The coefficients of the equation are calculated explicitly in terms of integrals containing linear stability characteristics of the flow. Stability of plane wave solutions of the Ginzburg-Landau equation is analysed. Numerical solutions of the Ginzburg-Landau equation are presented for different initial conditions. The second approach takes into account slow longitudinal variation of the base flow. The analysis is based on weakly nonparallel WKBJ approximation. A first-order amplitude evolution equation is derived. The solution of the amplitude equation is then used to obtain the first-order approximation in the perturbation field