We start from quantum mechanical laser equations which were derived in a previous paper for an inhomogeneously broadened laser and which contain in particular the noise sources due to cavity losses, vacuum fluctuations, interaction with phonons and nonlasing photons and the pump. For the example of frequency locking caused by the nonlinear polarization we derive a quantum mechanical Langevin equation for the relative phase angleψ=2ψ2 —ψ1-ψ3, whereψ1,ψ2,ψ3, are the total phases of three axial modes which would be equally spaced in the unloaded cavity. In the resulting equation $$\dot \psi = \delta - \beta \sin \psi + f(t)$$ (1) the fluctuating forcef(t) is Markoffian and Gaussian, the second moment being given by δ (t- t′)2(Γ1+Γ3+4Γ2), whereΓj is the linewidth of the individual unlocked mode,j. Eq. (1) is solved by Fokker-Planck techniques and numerical results are represented for the characteristic function of order 1. Furthermore the mean locking time is represented in a graphical plot. The results are also applicable to two modes which are coupled to each other, e.g. by loss modulation. In this case the second moment off (t) is given byδ(t-t′)2(Γ1+Γ2). Finally we discuss briefly an example of an experiment where the influence of noise on the frequency locking phenomenon may be observed.