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Recent advances on gamma-ray observations from SuperNova Remnants andMolecular Clouds offer the possibility to study in detail the properties of thepropagation of escaping Cosmic Rays (CR). However, a complete theory for CRtransport outside the acceleration site has not been developed yet. Twophysical processes are thought to be relevant to regulate the transport: thegrowth of waves caused by streaming instability, and possible wave dampingmechanisms that reduce the growth of the turbulence. Only a few attempts havebeen made so far to incorporate these mechanisms in the theory of CR diffusion.In this work we present recent advances in this subject. In particular, we showresults obtained by solving the coupled equations for the diffusion of CRs andthe evolution of Alfven waves. We discuss the importance of streaminginstabilities and wave damping in different ISM phases.

Non-linear Cosmic Ray propagation close to the acceleration site