  In this paper we extend the Lumer-Phillips theorem to the context of
two--parameter C_0-semigroup of contractions. That is, we characterize the
infinitesimal generators of two--parameter C_0-semigroups of contractions.
Conditions on the behavior of the resolvent of operators, which are necessary
and sufficient for the pair of operators to be the infinitesimal generator of a
C_0-semigroup of contractions are given.
