  A system of singularly perturbed ordinary differential equations of first
order with given initial conditions is considered. The leading term of each
equation is multiplied by a small positive parameter. These parameters are
assumed to be distinct and they determine the different scales in the solution
to this problem. A Shishkin piecewise--uniform mesh is constructed, which is
used, in conjunction with a classical finite difference discretization, to form
a new numerical method for solving this problem. It is proved that the
numerical approximations obtained from this method are essentially first order
convergent uniformly in all of the parameters.
