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We present a systematic analysis of archival HST WFPC2 ``Association'' datasets that correlate with the Chandra positions of a set of 44 ultra-luminousX-ray sources (ULXs) of nearby galaxies. We have improved the Chandra-HSTrelative astrometry whenever possible. Disparate numbers of potential ULXcounterparts are found, and in some cases none are found. The lack of or lownumber of counterparts in some cases may be due to insufficient depth in theWFPC2 images. Particularly in late-type galaxies, the HST image in the ULXregion was often complex or crowded. We therefore address various scenarios forthe nature of the ULX since it is not known which, if any, of the sources foundare true counterparts. The optical luminosities of the sources are typically inthe range 10^4-6 L_sun. In several cases color information is available, withthe colors roughly tending to be more red in early-type galaxies. This suggeststhat, in general, the (potential) counterparts found in early-type galaxies arelikely to be older stellar populations, and are probably globular clusters.Several early-type galaxy counterparts have blue colors, which may be due toyounger stellar populations in the host galaxies, however these could also bebackground sources. In spiral galaxies the sources may also be due to localizedstructure in the disks rather than bound stellar systems. Alternatively some ofthe counterparts in late-type galaxies may be isolated supergiant stars. Theobserved X-ray/optical flux ratio is diluted by the optical emission of thecluster in cases where the system is an X-ray binary in a cluster, particularlyin the case of a low-mass X-ray binaries in old cluster. (abridged)

Optical Counterparts of Ultraluminous X‐Ray Sources Identified from Archival HST WFPC2 Images