A methodology for solving the coupled linear flow and transport inverse problem is presented. It allows the estimation of aquifer parameters (transmissivity, storativity, recharge, boundary heads and flows, leakage, dispersivity, molecular diffusion, porosity, retardation, linear decay, boundary concentrations), using their prior estimates as well as head and concentration measurements as basic information. Transient flow and transport equations are solved using the finite element method in space and a weighted finite difference scheme in time. Flow and transport domains can be one-, two-, or quasi three-dimensional, applying linear one-dimensional elements, linear two-dimensional triangles, or bilinear two-dimensional rectangles mixed at will. Time regimes can be transient or steady state in any equation (flow or transport). Parameters are estimated on the basis of maximum likelihood theory, which allows us to obtain information about parameters' uncertainty. Minimization of the negative log likelihood is performed using Marquardt's method. The applicability of the method is shown by means of two real examples. They illustrate that the proposed approach can successfully address model selection, parameter uncertainty, and nontrivial identifiability problems. Estimation of time-dependent sources and the role of prior estimates are also addressed in the examples. While the formulation of the problem leaves room for both stochastic and deterministic treatment of hydraulic parameters, the latter has been adopted in both examples. Limitations of the approach are also apparent. ¿ American Geophysical Union 1996