The conventional Wood-Anderson Seismograph normally goes out of scale for strong local earthquakes. Also, the magnitude values determined from distant recordings may sometimes be in great error due to inaccuracies in the attenuation law used. Thus the Wood-Anderson Seismograms synthesized from strong-motion accelerograms recorded at close distances provide a useful basis for getting accurate and reliable values of local magnitudes. Using strong-motion data, local magnitudes for nineteen significant earthquakes in the Koyna dam area have been computed in the present study. The merits of the method used for computing the magnitudes from strong motion accelerograms in this study has been also discussed vis-a-vis the magnitude determinations based on Wood-Anderson records or the total coda durations as in the past.