We present results from a study of short term variability in 19 archival observations by XMM-Newton of 16 Ultraluminous X-ray Sources (ULXs). Eight observations (six sources) showed intrinsic variability with power spectra in the form of either a power law or broken power law-like continuum and in some cases quasi-periodic oscillations (QPOs). The remaining observations were used to place upper limits on the strength of possible variability hidden within. Seven observations (seven sources) yielded upper limits comparable to, or higher than, the values measured from those observations with detectable variations. These represented the seven faintest sources all with f_x < 3x10^-12 erg cm^-2 s^-1. In contrast there are four observations (three sources) that gave upper limits significantly lower than both the values measured from the ULX observations with detectable variations, and the values expected by comparison with luminous Galactic black hole X-ray binaries (BHBs) and Active Galactic Nuclei (AGN) in the observed frequency bandpass (10^-3 - 1 Hz). This is the case irrespective of whether one assumes characteristic frequencies appropriate for a stellar mass (10 M_sun) or an intermediate mass (1000 M_sun) black hole, and means that in some ULXs the variability is significantly suppressed compared to bright BHBs and AGN. We discuss ways to account for this unusual suppression in terms of both observational and intrinsic effects and whether these solutions are supported by our results. Comment: 12 pages, 5 figures, accepted by MNRAS