  We have searched for persistent radio pulsations, bright single pulses, and
bursts from four Southern anomalous X-ray pulsars (AXPs). Deep observations
were conducted at 1.4 GHz in 1999 July and August with the Parkes 64-m
telescope. For all of the target AXPs, the upper limits on integrated pulsed
emission are ~0.02 mJy, while the limits on the flux of single pulses are ~1 Jy
or better. The corresponding radio luminosity limits are significantly below
the observed luminosities of the majority of the observed radio pulsars, and
they are significantly below the radio luminosity of XTE J1810-197, the only
AXP known thus far to emit radio pulsations, at the epoch when radio pulses
were first detected from this source. Our null results support the hypothesis
that pulsed radio emission from AXPs is only present in conjunction with X-ray
outburst activity. However, we cannot rule out the possibility that pulsed
radio emission is present, but that it is too weak to be detected in our
observations, or that unfavorable viewing geometries prevent this emission from
being seen by terrestrial observers. Given the possible association between the
radio emission and transient X-ray behavior of XTE J1810-197, continued radio
searches of these and other AXPs at different epochs are warranted,
particularly after periods of X-ray burst activity.
