The stochastic properties of turbulent plasma waves are taken into account in the consideration of the
modulational instability. The limits of applicability of the theory of
weak plasma turbulence in the description of the modulational processes are
found. It is shown that this theory can be applied for the description of the
modulational interaction only for sufficiently wide wave spectra (and/or sufficiently low levels of
plasma turbulence) when the modulational interaction of different modes in the packet is small.
It is demonstrated that the development of the modulational interaction processes results
in rapid decrease of the wave stochasicity.