We present the results of Rossi X-ray Timing Explorer (RXTE) and Swift monitoring observations of the magnetar 1E 1547.0-5408 following the pulsars radiative outbursts in 2008 October and 2009 January. We report on a study of the evolution of the timing properties and the pulsed flux from 2008 October 4 through 2009 December 26. We show that the pulsed flux decrease which followed an initial rise in the 2008 outburst was interrupted by a spike ~9 days after the initial outburst. In our timing study, a phase-coherent analysis shows that for the first 29 days following the 2008 outburst, there was a very fast increase in the magnitude of the rotational frequency derivative nudot, such that the second derivative was a factor of ~60 larger than that reported in data from 2007. This nudot magnitude increase occurred in concert with the decay of the pulsed flux following the start of the 2008 event. Following the 2009 outburst, for the first 23 days, the second derivative was consistent with zero, and nudot had returned to close to its 2007 value. In contrast to the 2008 event, the 2009 outburst showed a major increase in persistent flux, relatively little change in the pulsed flux, and sudden significant spectral hardening ~15 days after the outburst. We show that, excluding the month following each of the outbursts, and because of the noise and the sparsity in the data, multiple plausible timing solutions fit the pulsars frequency behavior. We note similarities in the behavior of 1E 1547.0-5408 following the 2008 outburst to that seen in the AXP 1E 1048.1-5937 following its 2001-2002 outburst and discuss this in terms of the magnetar model.
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