Within the scope of a nonequilibrium statistical ensemble formalism we derive a hierarchy of equations of evolution for a set of basic thermo-hydrodynamic variables, which describe the macroscopic nonequilibrium state of a fluid of bosons. This set is composed of the energy density and number density and their fluxes of all order. The resulting equations can be considered as far-reaching generalizations of those in Mori＇s approach. They involve nonlocality in space and retro-effects (i.e. correlations in space and time respectively), are highly nonlinear, and account for irreversible behavior in the macroscopic evolution of the system. The different contributions to these kinetic equations are analyzed and the Markovian limit is obtained. In the follow up article we consider the nonequilibrium thermodynamic properties that the formalism provides.