The properties of X-ray variability from accreting black holes reveal much about conditions close to the event horizon. Observing common timing signals in many objects, suggests similarities within their accretion flows.\ud To further this aim this thesis presents a systematic survey of the short term variability properties in 19 observations of 16 Ultraluminous X-ray Sources (ULXs) taken with XMM-Newton using the power spectra. Significant short term variability is detected in 8 observations, but 4 of those remaining have upper limits on levels of variability below those observed in Galactic Black Hole Binaries (BHBs). Suggested causes for this suppression include large scale optically thick outflows destroying correlated variability from the source, or that the variability concentrated over shorter timescales than those studied here.\ud Tests for a positive linear correlation between the amplitude of variability (rms) and flux within an observation are presented for archival observations of 9 BHBs. Revealing that this relation is ubiquitous in the broad-band noise for all long, bright observations with sufficient variability to measure the rms. Interestingly, comparisons between the properties of the rms-flux relations over the course of many outbursts, reveal that the x-axis offsets become strongly positive as the source moves into the hard intermediate state.\ud The presence of a linear rms-flux correlation is also found in the light curve from a ULX (NGC 5408 X-1) and in some observations of the type C QP0 from the 1998 outburst of XTE 11550-564. In the latter case the rms-flux relation is found to be dependent on the frequency of the QPO, becoming constant or even negative once the QPO moves above ~5 Hz. A possible time lag between soft and hard emission is also identified from the ULX
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