The mathematical basis for two new computer codes, PULSER and PULMAT, is described. The PULSER code simulates the temporal and steady-state concentration profiles in pulsed column contactors using the Purex process. The CPU times needed for these calculations are at least 50 times less than those using the previously described CUSEP code. This is obtained by recognizing that effects due to pulsing occur on a much faster time scale than those due to steady flow and they can be approximated as occurring instantaneously. Separation of the time scales allows the formulation of simple flow equations for pulsed column contactors. In addition, a matrix method can be devised that makes possible direct calculation of the steady-state concentration profiles, resulting in very short CPU times. The code that performs these calculations is called PULMAT. Both codes have been used to generate concentration profiles in several extraction (A-type) and stripping (E-type) contactors and in a partitioning (B-type) contactor. These results are compared with results obtained using the CUSEP computer code and with other results where available.