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Existing sensitivity methods for spatially discrete groundwater contaminant transport models have been developed for time-stepping numerical algorithms and cannot be readily used with time-continuous approaches to transport simulation, such as the Laplace transform Galerkin technique. We develop direct and adjoint sensitivity methods in which sensitivity coefficients are computed in the Laplace domain and inverted numerically to the time domain. The methods are computationally efficient when used in conjunction with time-continuous transport equations. The relative efficiency of the two methods depends on the number of model parameters, number of performance measures, and number of spatial discretization nodes. The adjoint method is favored when the number of performance measures is much smaller than the number of model parameters. The adjoint method is limited in that performance measures are restricted to being linear functions of state variables. A two- dimensional transport example is developed in detail, and sensitivities with respect to nodal hydraulic conductivities are computed. In the problems analyzed, the direct and adjoint methods are 9 to 156 times faster than the perturbation method, with the computational savings increasing as the size of the problem is increased.