The nonlinear inverse method of Xie <1993> is applied to analyze Lg spectra from many recent underground nuclear explosions in central Asia. The analysis simultaneously determines Lg seismic moments (M0) and corner frequencies (fc) of events, as well as path-variable Lg Q values and their frequency dependences at 1 Hz. Lg Q at 1 Hz estimated for many paths from the Lop Nor and Balapan test sites to various broadband Incorporated Institution for Seismology, Chinese Digital Seismic Network, and Kyrghizstan Network stations agree well with path-averaged Lg coda Q values from previously obtained tomographic maps for Eurasia. This suggests that the Lg Q values obtained in this inversion have not been significantly affected by focusing/defocusing or other effects of three-dimensional structural complexities. The logarithms of Lg M0 values obtained in this study correlate linearly, with a slope of about 1.2, with International Seismological Centre (ISC) body wave magnitudes (Mb). The linear relationship is consistent with a previous empirical relationship found between the logarithm of P wave seismic moments and ISC Mb values. The slope of the linear relationship also suggests that the logarithm of Lg M0 is a more direct measure of event size than is Mb, which, for larger events, is affected by high-frequency amplitude falloff. Another important finding of this study is that the M0 values for the explosions scale with fc-4, rather than with fc-3, as would be expected if stress drops were constant. This is consistent with previous scaling relations derived using Lg from earthquake sources and suggests that the difference between Lg and local S excitation by the same source types (explosion or earthquake) may overwhelm that between the excitation of Lg by different source types. A comparison between Lg M0 and fc values obtained using an explosion source model with those obtained using an earthquake source model suggests that the M0 values estimated using the explosion source model are systematically lower (by a factor of 0.27) than those estimated using the earthquake source model. This occurs even though the data used are the same in the inversions with the two types of source model. The factor of 0.27 is therefore due to the source model dependence of the M0, fc estimates. The overshoot and lower spectral levels at lower frequencies in the explosion source model tend to reduce both the estimated M0 and fc values. This suggests that in any nuclear monitoring program, the same type of source model (either an earthquake or explosion) should always be used to discriminate explosions using Lg. The source model dependence also suggests that more effort should be made to estimate the amount of overshoot in the Lg excitation caused by various source types. ¿ American Geophysical Union 1996