The model matching problem for single-input single-output singularly perturbed systems is considered. Two sets of sufficient conditions are obtained to guarantee the existence of a two-frequency-scale solution : one for the optimal and one for a suboptimal case. Both the minimum-phase and the non-minumum-phase cases are treated. The sub-optimal two-frequency-scale solution constructed in this paper uses the solutions of two well-defined lower-order problems, and therefore it is numerically better conditioned and computationally less demanding than the traditional optimal methods. A two-stage algorithm for the computation of the suboptimal TFS solution is presented.