We detected a new AM Her star serendipitously in a 25 day observation with the EUVE satellite . A coherent period of 85.82 min is present in the EUVE Deep Survey imager light curve of this source . A spectroscopic optical identification is made with a 19th magnitude blue star that has H and He emission lines , and broad cyclotron humps typical of a magnetic cataclysmic variable . A lower limit to the polar magnetic field of 46 MG is estimated from the spacing of the cyclotron harmonics . EUVE J0425.6–5714 is also detected in archival ROSAT HRI observations spanning two months , and its stable and highly structured light curve permits us to fit a coherent ephemeris linking the ROSAT and EUVE data over a 1.3 yr gap . The derived period is 85.82107 \pm 0.00020 min , and the ephemeris should be accurate to 0.1 cycles until the year 2005 . A narrow but partial X-ray eclipse suggests that this object belongs to the group of AM Her stars whose viewing geometry is such that the accretion stream periodically occults the soft X-ray emitting accretion spot on the surface of the white dwarf . A non-detection of hard X-rays from ASCA observations that are contemporaneous with the ROSAT HRI shows that the soft X-rays must dominate by at least an order of magnitude , which is consistent with a known trend among AM Her stars with large magnetic field . This object should not be confused with the Seyfert galaxy 1H 0419–577 ( = LB 1727 ) , another X-ray/EUV source which lies only 3. ^ { \prime } 95 away , and was the principal target of these monitoring observations .