  We propose a non-perturbative solution of N=2 supersymmetric gauge theory in
five dimensions compactified on circle of a radius $R$. We consider the cases
of the pure gauge theory as well as the theories with matter in the fundamental
and in the adjoint representations. The pure theory as well as the one with
adjoint hypermultiplet give rise to the known relativistic integrable systems
with ${1\over{R}}$ playing the r\^ole of the speed of light. The theory with
adjoint hypermultiplet exhibits some interesting finiteness properties.
  Talk given at the III International Conference ``Conformal Field Theories and
Integrable Models'', Chernogolovka, June 23-30 1996
