International audienceThe microwave emission linewidth of spin transfer torque nano-oscillators is closely related to their phase and amplitude noise that can be extracted from the magnetoresistive voltage signal V(t) using single shot time domain techniques. Here we report on phase and amplitude noise studies for MgO based magnetic tunnel junction oscillators. The analysis of the power spectral densities allows one to separate the linear and nonlinear contributions to the phase noise, the nonlinear contribution being due to the coupling between phase and amplitude. The coupling strength as well as the amplitude relaxation rate can be directly extracted