  Spectroscopic observations of 51 Pegasi and tau Bootis show no periodic
changes in the shapes of their line profiles; these results for 51 Peg are in
significant conflict with those reported by Gray and Hatzes (1997). Our
detection limits are small enough to rule out nonradial pulsations as the cause
of the variability in tau Boo, but not in 51 Peg. The absence of line shape
changes is consistent with these stars' radial velocity variability arising
from planetary-mass companions.
