Attenuation of Lg waves is estimated using 61 events located in the subduction zone of the Middle American trench and recorded by the seismic network of Laguna Verde, Veracruz, Mexico. We estimate the anelastic attenuation coefficient &ggr; of Lg waves or, equivalently, QLg by calculating the rate of acceleration spectra decay with distance. We consider paths from two regions: Guerrero-Veracruz (NE-SW direction) and Oaxaca-Veracruz (North-South direction). Assuming a frequency dependence of &ggr; of the form &ggr;(f )=&ggr;0f&eegr;, we find that &eegr;=0.175¿0.05 for both regions and that &ggr;0 was lower for paths from Guerrero to Veracruz (&ggr;0=0.0071¿0.002) than for paths from Oaxaca to Veracruz (&ggr;0=0.0161¿0.003) in the frequency range from 2 to 7 Hz. In terms of the quality factor QLg, values of QLg=134¿30f0.83¿0.2 and QLg=59¿10f0.81¿0.2 were found for the Guerrero-Veracruz and the Oaxaca-Veracruz paths, respectively. This difference in attenuation may be due to the state of stresses that prevails in both regions including the density and fluid content of fractures, which are attenuation mechanisms also suggested for other regions <Mitchell, 1995>. ¿ 1997 American Geophysical Union