The most well-known formulation of the fluctuation-dissipation theorem (FDT) is states a proportionality between correlation and integrated response function of an observable at equilibrium. Actually in a large variety of out of equilibrium systems wich possess an invariant measure, a non linear relation beetween response and corresponding correlation is observed. This behaviour, sometimes claimed as a "violation of FDT", is due to correlation among different degrees of fredoom. We discuss how to link response function of these systems to a specific correlator of the steady state, restoring FDT in a more general form. By means of examples taken from Langevin dynamics and granular gases, we show how it is possible to verify ansatz on invariant measure's shape of these non equilibrium systems