  The instanton contributions to the partition function and to homologically
trivial Wilson loops for a U(N) Yang-Mills theory on a torus $T^2$ are
analyzed. An exact expression for the partition function is obtained as a sum
of contributions localized around the classical solutions of Yang-Mills
equations, that appear according to the general classification of Atiyah and
Bott. Explicit expressions for the exact Wilson loop averages are obtained when
N=2, N=3. For general $N$ the contribution of the zero-instanton sector has
been carefully derived in the decompactification limit, reproducing the sum of
the perturbative series on the plane, in which the light-cone gauge Yang-Mills
propagator is prescribed according to Wu-Mandelstam-Leibbrandt (WML). Agreement
with the results coming from $S^2$ is therefore obtained, confirming the truly
perturbative nature of the WML computations.
