The stability properties of an external cavity laser with strong grating-filtered optical feedback to an anti-reflection coated
facet are studied with a general frequency domain model. The model takes into account non-linear effects like four wave mixing and gain compression. A small-signal analysis in the frequency domain allows a calculation of the range of operation without mode hopping around the grating reflectivity peak. This region should be as large as possible for proper operation of the tunable laser source. The analysis shows the stabilizing effect of mode coupling and of gain compression on the lasing mode. An integral equation for the electrical field is derived from the frequency domain model and used for time domain simulations of large-signal behavior.