  We provide sufficient conditions of local solvability for partial
differential operators with variable Colombeau coefficients. We mainly
concentrate on operators which admit a right generalized pseudodifferential
parametrix and on operators which are a bounded perturbation of a differential
operator with constant Colombeau coefficients. The local solutions are intended
in the Colombeau algebra $\G(\Om)$ as well as in the dual
$\LL(\Gc(\Om),\wt{\C})$.
