Analytic solutions for two quasi-self-similar problems of the boundary layer theory in the weakly nonlocal approximation, are found. Explicit linear relationships are derived for the parameters of the nonlocal model, relating them to the integral parameters of the flow, such as flowrates or displacement thicknesses. This allows complete closure of the formulation of the problem at moderate values of the relative scale of relaxation of the internal structure of the medium. The suggested nonlocal model provides a uniform description of a number of phenomena actually observed in disperse flows by mean of the same class of solutions. (A)