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Reactive transport sometimes depends on the time of exposure of conveyed material to other materials present in the system. The distribution of groundwater age, the effects of mineral chemical heterogeneity on reactive solute transport, the occurrence of lag in bioreactive systems, and dose-dependent immunosuppression, are some areas that involve exposure-time in an important way. A balance equation for accounting for such effects is developed through an extended transport operator that incorporates generalized exposure-time as an additional structural variable. The general transport equation is derived from basic mass balance arguments, by treating the constituents as a mixture of overlapping continua and developing evolution equations for the mixture material densities in the extended dimensions of space, time, and exposure-time. A non-physical advection operation is used to track exposure of materials undergoing transport and non-equilibrium mass transformations. Constraints appearing from chemical thermodynamics on the forms of admissible differential equations are noted. Example applications are described.