## ABSTRACT

The grid approximations of a Dirichlet problem are considered for a system of two singularly perturbed elliptic reaction-diffusion equations with two perturbation parameters on a rectangle. For the data of the boundary value problem, compatibility conditions are given to ensure sufficient smoothness of the solution to the problem that is required for the construction and justification of schemes convergent uniformly with respect to the perturbation parameters ε2i , i = 1, 2. A priori estimates are constructed for the problem solution. Using these estimates, the condensing mesh technique and classical finite difference approximations of the problem, special finite difference schemes are constructed that converge ε21, ε

2 2-uniformly with the convergence order close

to 2.