We present in this paper a method of accurately solving the pure proportional navigation equations in closed form for maneuvering and nonmaneuvering targets. The method is based on a quasilinearization (QL) procedure. The explicit QL solutions presented here are shown to be a generalization of the classical linear (CL) solutions. This generalization results in an improvement in the estimation of missile lateral acceleration and enlarges the validity of the solutions to a wide range of engagement geometries and maneuver levels than is possible with the CL approach. The method outlined here is capable of generating explicit solutions for all trajectory angles, as well as the time of flight and lateral acceleration.