In this paper, we investigate general impulsive nonautonomous population dynamical systems of functional differential equations. By utilizing the method of multiple Liapunov-like functionals to construct the permanence region, a general criterion on the permanence for the system is established. Furthermore, as applications of this general criterion, a class of impulsive nonautonomous n-species Lotka-Volterra competitive systems with delays and a class of impulsive nonautonomous 3-species Lotka-Volterra food chain systems with delays are discussed. Some new and useful sufficient conditions on the permanence for these systems are established.