We present here a formulation of the resonant and nonresonant interactions among gravity waves, acoustic waves, and vortical modes in the atmosphere under the weak interaction approximation. This work generalizes previous studies by including the effects of rotation and wind shear. Rotation influences both wave and vortical mode structures, while wind shear is shown to influence the relative frequencies of gravity waves and vortical modes and thus may alter the conditions for gravity wave-vortical mode interactions occurring in its absence. The theory is applied in the absence of rotation and is shown to permit interactions that depend in complex manner on the gravity wave and vortical mode characteristics and relative orientation and on the mean wind shear. In a companion paper we apply this formalism in a study of the influences of variable stratification and inhomogeneity on resonant and nonresonant interactions. ¿ American Geophysical Union 1992