We consider the weakly nonlinear three-wave interactions in an isothermal atmosphere. The mutual interactions among the three linear branches of dynamical-thermodynamical atmospheric motions (gravity waves, acoustic waves, and vortical motions) are investigated. In addition to the resonant case, nonresonant interactions are also considered. On the basis of the analytical solution of the linearized wave-amplitude equation with possible existence of a frequency mismatch, the resonance surface, the interaction domain, and growth time in three-dimensional geometry in k-space in various cases have been calculated and some numerical results are given. It is found that the nonresonant interaction can be very important, especially when a gravity wave and two vortical modes of motions interact as a nonresonant trio. The energy transfer from the gravity wave to vortical motions might limit the growth of the gravity wave amplitude and hence might provide a reasonable mechanism for gravity waves to saturate in the middle atmosphere. ¿ American Geophysical Union 1988