We examine the evolution of three-gravdy-wave interactions, with one initaly much stronger Ihun the other two, in a dissipative atmosphere, The characteristic time is used as an essential lime ca e for depicting the interactions. In the absense of viscosity, the solutions of the lineatized interaction equations, viz., the paramettic instability, give a good description for the evolution of secondary waves up to one-hail ol the characteristic time Beyond this time, the linear solutions are invalid; the evolution must be obtained by solving the complete interaction equations For given initial wave amplitudes, the characteristic time increases with the increasing wavelength of the primary wave; thus the criterion for the validity of resonant interaction approximation may be better satisfied The viscous dissipation makes the characteristoc time larger, and when severe enough a porlion oftbe seuondary waves, particularly at high wavenumbers, may fail to interacl with the primary wave effectively Additionally. the maxima of the energy densities for the secondary wavve are smaller than those in the absence of viscosity. In the ease of a significalt frequeney mismatch, only a fraction of the primary wave energy lakes part in the hlterchange Copyright.