New asymptotic approximations of the equations modeling the stability of two coupled lasers are investigated. We show that instabilities leading to intensity oscillations are possible. We discuss the validity of each approximation and the mechanisms leading to these instabilities. For two coupled solid state lasers, an instability occurs when the frequency detuning surpasses a critical value and the difference between the phases of the laser fields is forced to be unbounded in time. For two coupled semiconductor lasers, it is the strong coupling between the phase and the laser intensity that is the mechanism leading to period doubling instabilities.