The general concepts of spin wave theory are adapted to the spin torque driven dynamics of a self-polarized system based on two layers coupled via interlayer exchange (conservative coupling) and mutual spin torque (dissipative coupling). An analytical description of the nonlinear dynamics is proposed and validated through numerical simulations. In contrast to the single layer model, the phase equation of the coupled system has a contribution coming from the dissipative part of the LLGS equation. It is shown that this is a major contribution to the frequencymandatory to describe well the most basic features of the dynamics of this coupled system.Using the proposed model a specific feature of coupled dynamics is addressed: the redshift to blueshift transition observed in the frequency current dependence of this kind of exchange coupled systems upon increasing the applied field. It is found that the blueshift regime can only occur in a region of field where the two linear eigenmodes contribute equally to the steady state mode (i.e., high mode hybridization). Finally, a general perturbed Hamiltonian equation for the coupled system is proposed.