Abstract <p>This article aims at the construction and analysis of a computational method for a system of two parameter singularly perturbed second order nonlinear differential equations with prescribed boundary conditions which modeling reaction-convection-diffusion processes. A fitted mesh method consists of a classical finite difference scheme together with a Shishkin mesh which is constructed to solve the system. The fitted mesh method is proved to be essentially first order convergent uniformly with respect to the perturbation parameters. An algorithm that involves the continuation method is designed to compute the numerical approximations. Numerical experiments support the theoretical results. As no literature is available on systems of two parameter singularly perturbed nonlinear differential equations, the present study reveals the characteristics of such systems and helps to solve them numerically.</p>