The pull-in range, known also as the acquisition or capture range, is an important characteristics of synchronization circuits such as phase-locked loops (PLL). The pull-in range characterizes the maximal frequency detuning under which phase locking is provided. The presence of periodic nonlinearities makes rigorous analysis of PLLs very difficult. The models of PLLs can be featured by hidden attractors and chaos. The pull-in range is typically estimated numerically. Analytic results primarily deal with ordinary differential equations. In this paper, we propose an analytic method for pull-in range estimation, applicable to synchronization systems with infinite-dimensional linear part, in particular, with delays.