The study of edge control problems for quasilinear integro-differential systems with pulsed action is an urgent area of modern mathematics, which is used in modeling complex dynamic processes. The main goal of studying the controllability of quasilinear integro-differential equations with pulsed action is to develop methods that allow determining the conditions under which the system is controllable, to develop algorithms that allow you to build control actions to implement the desired trajectory of the system, and to investigate the stability of solutions under conditions of both regular and abrupt external changes. This article discusses some conditions of controllability of the boundary value problem for a qua zilinear system of integro-differential equations with pulsed action. Processes in which pulsed action does not occur at pre-prescribed time points, but in mo time points, which are determined by the state of the system, have been investigated. The article proved some conditions of controllability of quasilinear integro-differential equations with pulsed action in the form of lemmas, a definition of solvability of the control problem is given.