  We discuss the N=2 SU(2) Yang-Mills theory coupled with a massive matter in
the weak coupling. In particular, we obtain the instanton expansion of its
prepotential. Instanton contributions in the mass-less limit are completely
reproduced. We study also the double scaling limit of this massive theory and
find that the prepotential with instanton corrections in the double scaling
limit coincides with that of N=2 SU(2) Yang-Mills theory without matter.
