In this work, the variation of the local magnitude, MLSM, derived from strong-motion records at short distances is examined, in terms of moment magnitude, MW. Strong-motion data from Greek earthquakes are used to determine the strong-motion local magnitude, MLSM, by performing an integration of the equation of motion of the Wood-Anderson (WA) seismograph subjected to an input acceleration. The most reliable strong-motion data are utilized for earthquakes with seismic moments log M0 ≧ 22.0 dyne · cm and calculated local magnitudes, MLSM ≧ 3.7. The correlation between the seismic moments, log M0, and the calculated local magnitudes, MLSM, using strong-motion records is given by log M0 = 1.5*MLSM + 16.07, which is very similar to that proposed by Hanks and Kanamori (1979). Moreover, it is shown that MLSM is equal to moment magnitude, MW, for a large MLSM range (3.9 to 6.6). Comparison of the strong-motion local magnitude and the ML magnitude estimated in Greece (MLGR) and surrounding area shows a systematic bias of 0.4 to 0.5, similar to the difference that has been found between MW and MLGR for the same area. The contribution of the local site effects in the calculation of the local magnitude, MLSM, is also considered by taking into account two indices of soil classification, namely, rock and alluvium or the shear-wave velocity, v30s, of the first 30 m, based on NEHRP (1994) and UBC (1997). An increase of MLSM by 0.16 is observed for alluvium sites. Alternative relations showing the MLSM variation with, v30s are also presented. Finally, examination of the WA amplitude attenuation, −log A0, with distance shows that the Jennings and Kanamori (1983) relation for Δ < 100 km is appropriate for Greece. The same results confirm earlier suggestions that the 0.4 to 0.5 bias between MLGR and MW (also MLSM) should be attributed to a low static magnification (∼800) of the Athens WA instrument on which all other ML relations in Greece have been calibrated.