We observed four southern AXPs in 1999 near 1400 MHz with the Parkes 64-m radio telescope to search for periodic radio emission. No Fourier candidates were discovered in the initial analysis, but the recent radio activity observed for the AXP XTE J1810-197 has prompted us to revisit these data to search for single radio pulses and bursts. The data were searched for both persistent and bursting radio emission at a wide range of dispersion measures, but no detections of either kind were made. These results further weaken the proposed link between rotating radio transient sources and magnetars. However, continued radio searches of these and other AXPs at different epochs are warranted given the transient nature of the radio emission seen from XTE J1810-197, which until very recently was the only known radio-emitting AXP.
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