The article analyzes the evolution of the main single-mode stationary flow of a viscous incompressible fluid in a flat diffuser (with a constant sign in the flow velocity depending on the aperture angle of the diffuser) in the classical formulation of the Jeffrey — Hamel problem. Depending on the determining parameters (the diffuser angle and the Reynolds number), a complete solution of the problem is given. The transition of main single-mode flow at a fixed angle of the diffuser to the multimode modes (where the velocity of flow changes sign depending on the angle of the diffuser) when the Reynolds number has been changed is shown. It is found that starting from a certain critical value of the Reynolds number, the existence of a stationary single-mode flow is impossible. The corresponding bifurcation diagram is constructed and the dependence of this critical value vs. the aperture angle of diffuser is found. The possibility of realization of both single-mode and multimode flows at the same Reynolds number is shown. The parameters of the second and third bifurcation domains are also calculated.