  The focus of NASA's Swift telescope has been transients and
target-of-opportunity observing, resulting in many observations of
ultraluminous X-ray sources (ULXs) over the last ~20 years. For the vast
majority of these observations, simultaneous data has been obtained using both
the X-ray telescope (XRT) and the ultraviolet and optical telescope (UVOT),
providing a unique opportunity to study coupled variability between these
bands. Using a sample of ~40 ULXs with numerous repeat observations, we extract
stacked images to characterise the spatial extent of the UV-Optical emission
and extract long-term light curves to search for first-order linear
correlations between the UV and X-ray emission. We find that a small subset may
show weakly correlated joint variability, while other sources appear to display
non-linear relationships between the bands. We discuss these observations in
the context of several theoretical models: precession, irradiation of the outer
accretion disc and irradiation of the companion star. We conclude that more
complicated analysis or higher quality data may be required to accurately
constrain the nature of the joint X-ray and UV/optical emission in these
sources.
