  In this reply to the comment by C. R. Willis, we show, by quoting his own
statements, that the simulations reported in his original work with Boesch
[Phys. Rev. B 42, 2290 (1990)] were done for kinks with nonzero initial
velocity, in contrast to what Willis claims in his comment. We further show
that his alleged proof, which assumes among other approximations that kinks are
initially at rest, is not rigorous but an approximation. Moreover, there are
other serious misconceptions which we discuss in our reply. As a consequence,
our result that quasimodes do not exist in the sG equation [Phys. Rev. E 62,
R60 (2000)] remains true.
