  As a study of peculiar velocities of nonlinear structure, we analyze the
model of a relativistic thin-shell void in the expanding universe. (1) Adopting
McVittie (MV) spacetime as a background universe, we investigate the dynamics
of an uncompensated void with negative MV mass. Although the motion itself is
quite different from that of a compensated void, as shown by Haines & Harris
(1993), the present peculiar velocities are not affected by MV mass. (2) We
discuss how precisely the formula in the linear perturbation theory applies to
nonlinear relativistic voids, using the results in (1) as well as the previous
results for the homogeneous background (Sakai, Maeda, & Sato 1993). (3) We
re-examine the effect of the cosmic microwave background radiation. Contrary to
the results of Pim & Lake (1986, 1988), we find that the effect is negligible.
We show that their results are due to inappropriate initial conditions. Our
results (1)-(3) suggest that the formula in the linear perturbation theory is
approximately valid even for nonlinear voids.
