Numerical models for solving reactive solute transport in groundwater are often based on standard Eulerian methods, such as finite elements (FE). In this work, we combine the moving mesh Eulerian Lagrangian Localized Adjoint Method (ELLAM) with the direct substitution approach (DSA) and the sequential non-iterative approach (SNIA) to accurately solve advection dominated problems including chemical reactions. Performances of ELLAM are evaluated in comparing SNIA_ELLAM and DSA_LLAM to SNIA_FE and DSA_FE for (1) kinetic reactions with first-order decay, Monod bodegradation, and interphase mass transfer problems and (2) equilibrium reactions with linear and nonlinear sorption problems. DSA_ELLAM (respectively SNIA_ELLAM) is shown to be more efficient and accurate than DSA_FE (respectively SNIA_FE). For the test cases with kinetics, SNIA_ELLAM is highly accurate and efficient. However, for equilibrium reactions, it induces numerical diffusion and DSA_ELLAM reveals the more efficient and accurate method. (c) 2007 American Institute of Chemical Engineers.