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We present Chandra X-ray Observatory ACIS-S3 X-ray imaging observations andVLT/FORS2 and Hubble Space Telescope optical observations of two low-densityGalactic globular clusters; NGC 6366 and M55. We detect 16 X-ray sources with0.5-6.0 keV luminosities above Lx=4E30 erg/s within the half-mass radius ofM55, of which 8 or 9 are expected to be background sources, and 5 within thehalf-mass radius of NGC 6366, of which 4 are expected to be background sources.Optical counterparts are identified for several X-ray sources in both clustersand from these we conclude that 3 of the X-ray sources in M55 and 2 or 3 of theX-ray sources in NGC 6366 are probably related to the cluster. Combining theseresults with those for other clusters, we find the best fit for a predictednumber of X-ray sources in a globular cluster Nc=1.2 Gamma+1.1 Mh, where Gammais the collision number and Mh is (half of) the cluster mass, both normalizedto the values for the globular cluster M4. Some sources tentatively classifiedas magnetically active binaries are more luminous in X-rays than the upperlimit of Lx~0.001Lbol of such binaries in the solar neighbourhood. Comparisonwith XMM and ROSAT observations lead us to conclude that the brightest X-raysource in M55, a dwarf nova, becomes fainter in X-rays during the opticaloutburst, in accordance with other dwarf novae. The brightest X-ray source inNGC 6366 is a point source surrounded by a slightly offset extended source. Theabsence of galaxies and Halpha emission in our optical observations arguesagainst a cluster of galaxies and against a planetary nebula, and we suggestthat the source may be an old nova.

X-ray and optical observations of M55 and NGC 6366: evidence for primordial binaries