The space transformation method is applied to stochastic partial differential equations whose coefficients are random functions of space and/or time. Such equations constitute an integral part of groundwater flow and solute transport. A perturbation analysis based on Feynman- diagram expansions is proposed. This approach incorporates important information on spatial variability and fulfills essential physical requirements, both important advantages over ordinary hydrologic perturbation techniques. Moreover, the diagram-expansion approach reduces the original stochastic flow problem to a closed set of equations for the mean and the covariance function.