  We continue to construct lattice super Yang-Mills theories along the line
discussed in the previous papers \cite{sugino, sugino2}. In our construction of
${\cal N}=2, 4$ theories in four dimensions, the problem of degenerate vacua
seen in \cite{sugino} is resolved by extending some fields and soaking up
would-be zero-modes in the continuum limit, while in the weak coupling
expansion some surplus modes appear both in bosonic and fermionic sectors
reflecting the exact supersymmetry. A slight modification to the models is made
such that all the surplus modes are eliminated in two- and three-dimensional
models obtained by dimensional reduction thereof. ${\cal N}=4, 8$ models in
three dimensions need fine-tuning of three and one parameters respectively to
obtain the desired continuum theories, while two-dimensional models with ${\cal
N}=4, 8$ do not require any fine-tuning.
