Using data from the public archive of the Extreme- Ultraviolet Explorer (E U VE) all-sky survey, we have systematically searched for extreme-ultraviolet (EUV) emission (58-174 A, 0.07-0.21 keV) around approximately 2500 distinct positions in the sky corresponding to known X-ray-emitting extragalactic sources. We find that 20 X-ray galaxies are EUV bright and were detected with a significance above 4,:r during the EUVE survey: eight are reported here for the first time (MS 0037.7-0156, Mrk 142, M65, EXO 1128.1+6908, M87, Mrk 507, PKS 2005-489, and 1H 2351 -315.A). Sixty-eight additional galaxies are detected with a lower significance (3 <(y<4), but the list is affected by a high percentage of spurious sources. We comment on the properties of the eight new EUV galaxies (six Seyfert galaxies and two BL Lacertae objects) and discuss their possible spectral shapes at EUV wavelengths.