The evolution of homogeneous grid-generated turbulence in stratified fluid is investigated analytically. A small parameter decomposition on inverse Froude number is applied to the theory of nearly homogeneous turbulence developed earlier in refs. [1] and [2]. Applying the multiple scale method we calculate the frequency and amplitude of internal gravity waves and formulate differential system describing the wave-averaged behaviour of turbulence characteristics. The comparison with the numerical results published in (?1 and with known experimental data shows a very good agreement as to internal waves as to small scale turbulence in collapsed state. The long-term turbulence evolution in weakly stratified media can be regarded as a singular perturbation problem permitting us to gain an insight into the interaction between gravity waves and active turbulence.