Abstract: In the light of an idea that the dynamics of gravity waves in the middle and upper atmosphere is determined jointly by nonlinear interaction and molecular disspation, a set of equations depicting the nonlinear interactions of gravity waves in a dissipative atmosphere is derived in the frame of weak nonlinear theory. The equations can be used to study both interactions of fixed-phase and random-phase gravity wave packets. Starting from the equations we investigate the interaction of three discrete gravity wave packets. When an intense large-scale primary gravity wave propagates through the dissipative atmosphere, it likely decays into secondary waves through three wave interactions. The amplitudes of the secondary waves grow exponentially. The molecular dissipation and frequency dismatch yield a threshold value of horizontal fluid velocity associated with primary wave, only above this threshold the exponential growth of the amplitudes of the secondary waves can set in. The threshold value takes its mininum under the condition of resonance. The frequency dismatch leads to a variation in the intrinsic frequencies of the secondary waves. The magnitude of the variation is just a half of the dismatch value.