  Waves propagating inwardly to the wave source are called antiwaves which have
negative phase velocity. In this paper the phenomenon of negative phase
velocity in oscillatory systems is studied on the basis of periodically paced
complex Ginzbug-Laundau equation (CGLE). We figure out a clear physical picture
on the negative phase velocity of these pacing induced waves. This picture
tells us that the competition between the frequency $\omega_{out}$ of the
pacing induced waves with the natural frequency $\omega_{0}$ of the oscillatory
medium is the key point responsible for the emergence of negative phase
velocity and the corresponding antiwaves. $\omega_{out}\omega_{0}>0$ and
$|\omega_{out}|<|\omega_{0}|$ are the criterions for the waves with negative
phase velocity. This criterion is general for one and high dimensional CGLE and
for general oscillatory models. Our understanding of antiwaves predicts that no
antispirals and waves with negative phase velocity can be observed in excitable
media.
