Abstract: Aset of the interaction equations of inertial gravity waves in a dissipative atmosphere on the basis of the weak nonlinear theory is derived. This work generalizes previous studies by including the effects of spatial propagation, viscous dissipation and continuous spectrum. It is shown that the wave dissipation rate produced by viscosity depends on the spatial scale and propagation direction of inertial gravity waves. Coriolis effect makes the interaction coefficients complex. Starting from the equations we examined the parametric instability of inertial gravity waves. It is indicated that there exists a threshold of primary wave amplitude. The magnitude of the threshold is proportional to the dissipation rate of secondary waves. When the primary wave amptitude exceeds the threshold, the secondary waves grow exponentially.The interaction brings about a variation in the frequencies of the secondary waves. The magnitude of the variation is proportional to the energy density of the primary wave.