  We present the broad-band noise structure of selected Anomalous X-Ray Pulsars
(AXPs) and Soft Gamma Repeaters (SGRs) in the 2-60 keV energy band. We have
analyzed Rossi X-ray Timing Explorer Proportional Counter Array archival light
curves for four AXPs and one SGR. We detect that the persistent emission of
these sources show band limited noise at low frequencies in the range
0.005-0.05 Hz varying from 2.5% to 70% integrated rms in times of prolonged
quiescence and following outbursts. We discovered band-limited red noise in 1E
2259+586 only for $\sim$2 years after its major 2002 outburst. The system shows
no broad-band noise otherwise. Although this rise in noise in 1E 2259+586
occurred following an outburst which included a rotational glitch, the other
glitching AXPs showed no obvious change in broad-band noise, thus it does not
seem that this noise is correlated with glitches. The only source that showed
significant variation in broad-band noise was 1E 1048.1-5937, where the noise
gradually rose for 1.95 years at a rate of $\sim$3.6% per year. For this source
the increases in broad-band noise was not correlated with the large increases
in persistent and pulsed flux, or its two short SGR-like bursts. This rise in
noise did commence after a long burst, however given the sparsity of this
event, and the possibility that similar bursts went unnoticed the trigger for
the rise is noise in 1E 1048.1-5937 is not as clear as for 1E 2259+586. The
other three sources indicate a persistent band-limited noise at low levels in
comparison.
