Summary: In this paper, we shall study the existence and approximation results for a nonlinear two point boundary value problem of a second order ordinary differential equation with general form of Dirichlet/Neumann type boundary conditions. The nonlinearity present on right hand side of the differential equation is assumed to be Carathéodory containing a deviating argument. The proofs of the main results are based on a monotone iteration method contained in the hybrid fixed point principles of the first author [Tamkang J. Math. 45, No. 4, 397–426 (2014; Zbl 1343.45004)] in an ordered Banach space. Finally, some remarks concerning the merits of our monotone iteration method over other frequently used iteration methods in the theory of nonlinear differential equations are given in the conclusion.