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We provide sufficient conditions of local solvability for partialdifferential operators with variable Colombeau coefficients. We mainlyconcentrate on operators which admit a right generalized pseudodifferentialparametrix and on operators which are a bounded perturbation of a differentialoperator with constant Colombeau coefficients. The local solutions are intendedin the Colombeau algebra $\G(\Om)$ as well as in the dual$\LL(\Gc(\Om),\wt{\C})$.

Sufficient conditions of local solvability for partial differential operators in the Colombeau context