Generalized Taylor dispersion theory is herein extended to circumstances for which the transport of dissolved or suspended chemically reactive (as well as inert) solutes is affected by carrier-solvent flow fields and/or external forces that are time periodic in both their global and local microscale spaces (and possess commensurate frequencies). The local-space- and time-averaged solute transport process is characterized by three time-independent, but frequency-dependent microscale phenomenological coefficients - K̄*, Ū*, and D̄*, representing the mean chemical reaction rate, velocity vector, and dispersivity dyadic of the solute, respectively. These macroscale transport coefficients are expressed in terms of time-periodic eigenfunctions and corresponding eigenvalues using a recently developed solution scheme. This scheme permits the analysis of phenomena involving time-periodic transport coefficients on a par with that for the classical case of time-independent microscale phenomenological coefficients. The analysis generalizes to time-periodic local-space phenomena a previous treatment, in which only the global-space coefficients were allowed to vary periodically with time. This greatly enlarges the scope of potential applications of the analysis. In addition to the time-averaged phenomenological coefficients K̄*, Ū*, and D̄*, comparable instantaneous coefficients are defined governing the local-space-averaged instantaneous solute concentration. In contrast with their time-averaged counterparts, K̄*, Ū*, and D̄*, the latter instantaneous transport coefficients are shown to depend upon the initial solute distribution within the local space. Because of coupling between the local- and global-space transport processes in oscillatory flows and/or oscillatory external force fields, all harmonics of the resulting global-space solute velocity field contribute to the mean convective solute transport. This phenomenon may result, for example, in zero solvent-nonzero solute net macroscale transport (or vice versa). The driving frequency of the local-space time-periodic transport process may be used to parametrically control the macroscale solute reactivity rate coefficient, as well as the solute's mean velocity and dispersivity about that mean. A companion paper (Part II) [Phys. Fluids A 2, 1744 (1990)], provides an example, albeit for the nonreactive case.