  Vacuum structures of supersymmetric (SUSY) Yang-Mills theories in $1+1$
dimensions are studied with the spatial direction compactified. SUSY allows
only periodic boundary conditions for both fermions and bosons. By using the
Born-Oppenheimer approximation for the weak coupling limit, we find that the
vacuum energy vanishes, and hence the SUSY is unbroken. Other boundary
conditions are also studied, especially the antiperiodic boundary condition for
fermions which is related to the system in finite temperatures. In that case we
find for gaugino bilinears a nonvanishing vacuum condensation which indicates
instanton contributions.
