All-fiber Raman lasers have demonstrated their potential for the efficient conversion of highly multimode pump beams into a high-quality Stokes beams. However, the modal content of these beams has not been investigated yet. Here we apply, for the first time, a mode decomposition technique for revealing intermodal interactions in different operational regimes of CW multimode Raman lasers. Our approach allows for analyzing the output laser radiation in terms of the amplitude and phase distributions of a huge number of excited modes for both the pump and the Stokes beams, which enables a new insight into nonlinear mode coupling processes. The measured contribution of the first three modes of the residual pump beam after overcoming the SRS threshold decreased on average by 25%, whereas the signal beam mainly consists of fundamental mode (40%) and the modes of the first group (20%).