It is shown, first, that Ekman dissipation plays a stabilizing role in the development of perturbations in a zonal shear flow, by contracting the instability domain of linear theory and by lowering the saturation level for unstable perturbations. Second, it is shown that dissipation introduces a new scale and, consequently, a new type of critical layer (CL) called “the λ-CL” and provides, in a certain parameter domain, a modification of the nonlinear CL called “the λ-nonlinear CL.” There are consequently five CL regimes. For each regime the corresponding nonlinear evolution equation is obtained and the saturation level is calculated. Using these equations it is shown that a perturbation can develop according to one of six scenarios, each of which is described in detail.