Consideration was given to the single-frequency oscillations of the periodic system allied to the nonlinear multidimensional autonomous system. It was assumed that the generating autonomous system admits a family of solutions with period depending on a single parameter: all points of the family break down into the ordinary points whose derivative of the period with respect to the parameter is other than zero and the critical points where this derivative vanishes. Generation of oscillations and their stability at the ordinary point of the family were studied. These problems were solved earlier for the second-order system.