  A singularly perturbed linear system of second order ordinary differential
equations of reaction-diffusion type with given boundary conditions is
considered. The leading term of each equation is multiplied by a small positive
parameter. These parameters are assumed to be distinct. The components of the
solution exhibit overlapping layers. Shishkin piecewise-uniform meshes are
introduced, which are used in conjunction with a classical finite difference
discretisation, to construct two numerical methods for solving this problem. It
is proved that the numerical approximations obtained with these methods are
essentially first, respectively second, order convergent uniformly with respect
to all of the parameters.
