We study the dynamic behaviour of a coherently pumped single-mode unidirectional ring laser with an active medium of Doppler broadened three-level atoms. Our formulation is based on a set of 9N+1 real equations of the plane-wave mean-field Maxwell-Bloch type (N is the number of velocity groups of molecules considered). This model predicts, for a parameter range of the type explored in the experiments by Weiss and Brock (Phys. Rev. Lett. 57 (1986) 2804), a behaviour that reproduces most of their main experimental features. These include the instability pump threshold and the sequence of instabilities ocurring on resonator tuning and on increasing pump strength