We report on long-term monitoring of anomalous X-ray pulsars (AXPs) using the Rossi X-ray Timing Explorer (RXTE). Using phase-coherent timing, we find a wide variety of behaviors among the sources, ranging from high stability (in 1E 2259.1+586 in quiescence and 4U 0142+61), to instabilities so severe that phase-coherent timing is not possible (in 1E 1048.1-5937). We note a correlation in which timing stability in AXPs decreases with increasing $dot{ u}$. The timing stability of soft gamma repeaters (SGRs) in quiescence is consistent with this trend, which is similar to one seen in radio pulsars. We find no significant pulse morphology variations in any AXP in quiescence. We considered high signal-to-noise average pulse profiles for each AXP as a function of energy. We show that, as in the timing properties, there is a variety of different behaviors for the energy dependence. We also used the monitoring and archival data to obtain pulsed flux time series for each source. We have found no large changes in pulsed flux for any source in quiescence, and have set $1sigma$ upper limits on variations ~20-30% depending on the source. We have recently discovered bursts from the direction of two AXPs: 1E 1048.1-5937 the most SGR-like AXP, and 1E 2259.1+586 the most rotationally stable AXP. We compare the temporal, spectral and flux properties of these events to those of SGR bursts, and show that the two phenomena are very similar. These results imply a close relationship between AXPs and SGRs, with both being magnetars.
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