One of the five lines of evidence used by McKay et al. (1996) for relic life in the Martian meteorite Allan Hills (ALH) 84001 was the presence of objects thought to be microfossils. These ovoid and elongated forms are similar to structures found in terrestrial rocks and described as "nanobacteria" (Folk, 1993; McBride et al., 1994). Using the same procedures and apparatus as McKay et al. (1996), we have found structures on internal fracture surfaces of lunar meteorites that cannot be distinguished from the objects described on similar surfaces in ALH 84001. The lunar surface is currently a sterile environment and probably always has been. However, the lunar and Martian meteorites share a common terrestrial history, which includes many thousands of years of exposure to Antarctic weathering. Although we do not know the origin of these ovoid and elongated forms, we suggest that their presence on lunar meteorites indicates that the objects described by McKay et al. (1996) are not of Martian biological origin.