SUMMARYA homogeneous and internally consistent body of regional magnitudes is needed not only for the statistical study of seismicity but also for the modelling of seismic sources and for the hazard assessment of engineering sites. Also the assessment of the design ground motions for engineering projects requires homogeneous magnitude estimates. The nature of the available data for U.K. and Northwestern European earthquakes, and of the events themselves, is such that we are concerned with the assessment of magnitudes at the lower end of the scale, and thus great importance focuses on the uniform calculation of magnitudes within a relatively narrow range of M values. The purpose of this study is to present the uniform re-assessment of magnitudes for Britishand Northwestern European earthquakes for the period 1900 to 1984. It is shown that, for the larger events, surface-wave magnitudes can be estimated uniformly and that neither a period constraint at 20 seconds nor distance effects for the regional conditions considered appear to play an important role. For smaller events, crustal phases at short distances have been used to derive calibration curves for a magnitude which, at larger distances and longer periods would fit the magnitude scale of surface waves.