We report the results from observations of the BL Lac object EXO 05562
5 - 3838.6 carried out,in the X-ray band using ROSAT and ASCA during 1
993 and 1995. These observations provide the first X-ray spectra of th
e source obtained using image detectors. We find no evidence for drama
tic variability within either observation, but find the source to have
varied by a factor of similar to 1.5 in intensity between the two epo
chs. For both epochs we find the spectrum to be well described by a si
mple power-law model with a (photon) index Gamma similar to 2.5, absor
bed by an effective hydrogen column consistent with 21 cm measurements
along the line of sight through our Galaxy. EXO 055625 - 3838.6 lies
within the error box of the target designated H0557 - 385, similar to
25' south of the Seyfert 1 Galaxy included in the X-ray log N-log S an
d luminosity function derived from HEAOI data (Piccinotti et al. 1982)
. However, based upon the results presented here, we suggest the BL La
c object probably did not contribute significantly to earlier hard X-r
ay observations made using collimated instruments.