In the present paper, the problem of stabilizing a family of program motions of a bilinear nonstationary system with the help of a nonlinear full-order state descriptor for this system and a nonlinear Luenberger descriptor is considered. Methods to synthesize such descriptors and to construct a multiprogram stabilizing control in the form of nonlinear feedback are suggested. Theorems on sufficient conditions for the existence of a solution of the above problem are proved.