We apply the generalized quasilinearization method to a second order three-point boundary value problem involving mixed nonlinear boundary conditions and obtain a monotone sequence of approximate solutions converging to the unique solution of the problem possessing a convergence of order k(k� 2). 1. Introduction. The method of quasilinearization developed by Bellman and Kalaba (1) and generalized by Lakshmikantham (2-3) later on, has been studied and extended in several diverse disciplines. In fact, it is generating a rich history and an extensive bibliography can be found in (4-10). Multi-point nonlinear boundary value problems, which refer to a different family of boundary conditions in the study of disconjugacy theory (11), have been addressed by many authors, for example, see (12-14). In particular, Eloe and Gao (15) dis- cussed the quasilinearization method for a three-point boundary value problem. In this paper, we study the generalized quasilinearization method for a second order three-point boundary value problem with mixed nonlinear boundary conditions. In fact, a sequence of approximate solutions converging monotonically to a solution of the nonlinear three-point problem with the order of convergence k(k ≥ 2) has been presented.