We present a cross-correlation between the European Large Area ISO Survey (ELAIS) 15-μm ISO survey with the ROSAT (0.1-2keV) all-sky survey and the pointed observations WGACAT source catalogue. The resulting sample contains 15 objects. Optical spectroscopic identifications exist for 13 objects: six broad-line quasi-stellar objects (QSOs), four narrow-line galaxies (NLGs) or type 2 active galactic nuclei (AGN) and three stars. We have used both the X-ray to infrared (IR) luminosity flux ratio fx/fIR and the X-ray hardness ratios diagnostics to estimate the amount of obscuration in these objects. The X-ray spectrum of the narrow-line galaxies does not present strong evidence for obscuration; however, the low fx/fIR ratio combined with the high X-ray luminosities suggest that at least one of the NLGs is associated with an obscured Seyfert nucleus. Four out of the six QSOs present high fx/fIR ratios and steep X-ray spectra with Γ>2. One QSO (ELAISC15-J133442+375736) at a redshift of z=1.89, has an abnormally low X-ray/IR flux ratio, with its infrared luminosity approaching that of an hyperluminous galaxy (~1012.98h-2Lsolar). Finally, one radio-loud QSO is the hardest X-ray source in our sample, presenting strong evidence for a high absorbing column (NH~1022cm-2).