  Space-time wave packets can propagate invariantly in free space with
arbitrary group velocity thanks to the spatio-temporal correlation. Here it is
proved that the space-time wave packets are stable in dispersive media as well
and free from the spread in time caused by material dispersion. Furthermore,
the law of anomalous refraction for space-time wave packets is generalized to
the weakly dispersive situation. These results reveal new potential of
space-time wave packets for the applications in real dispersive media.
