The paper deals with a multidimensional control system, composed of a stable linear block and periodic nonlinear feedback. Such systems are called synchronization or pendulum-like systems. Synchronization systems often have multiple equilibria. The central problem concerned with dynamics of synchronization system is the convergence of all solutions to equilibria points (gradient-like behavior). For gradient-like systems the problem of cycle-slipping arises, which means that the solution may leave the basin of the nearest equilibrium and converge to another equilibrium point. This paper is addressed to synchronization systems with external disturbances. By means of Lyapunov periodic functions and Kalman-YakubovichPopov lemma the frequency-algebraic estimates for the number of slipped cycles are offered.