  We report on long-term monitoring of the anomalous X-ray pulsar (AXP) 1E
1048.1-5937 using the Rossi X-ray Timing Explorer (RXTE). The timing behavior
of this pulsar is different from that of other AXPs being monitored with RXTE.
In particular, we show that the pulsar shows significant deviations from simple
spin-down such that phase-coherent timing has not been possible over time spans
longer than a few months. We find that the deviations from simple spin down are
not consistent with single "glitch" type events, nor are they consistent with
radiative precession. We show that in spite of the rotational irregularities,
the pulsar exhibits neither pulse profile changes nor large pulsed flux
variations. We discuss the implications of our results for AXP models. In the
context of the magnetar model, we suggest that 1E 1048.1-5937 may be a
transition object between the soft gamma-ray repeater and AXP populations, and
the AXP most likely to one day undergo an outburst.
