Abstract. The paper describes the theoretical framework for a class of general continuous models of the hydrologic response including both flow and transport of reactive solutes. The approach orders theoretical results appeared in disparate fields into a coherent theoretical framework for both hydrologic flow and transport. In this paper we focus on the Lagrangian description of the carrier hydrologic runoff and of the processes embedding catchment-scale generation and transport of matter carried by runoff. The former defines travel time distributions, while the latter defines lifetime distributions, here thought of as contact times between mobile and immobile phases. Contact times are assumed to control mass transfer in a well-mixed approximation, appropriate in cases, like in basin-scale transport phenomena, where the characteristic size of the injection areas is much larger than that of heterogeneous features. As a result, we define general mass-response functions of catchments which extend to transport of matter geomorphologic theories of the hydrologic response. A set of examples is provided to clarify the theoretical results towards a computational framework for generalized applications, described in a companion paper.