The 7 s X-ray pulsator 1E 2259+586 was observed for approximately 1 da
y in 1993 with ASCA. Observations were also obtained with BBXRT in 199
0 a few months after Ginga had observed 1E 2259+586 to be brighter tha
n normal and the BBXRT data show 1E 2259+586 to be at an intermediate
brightness level. By contrast, the ASCA data appear to have been obtai
ned during a more common lower luminosity state. The pulse profiles we
obtain are consistent with a connection between flux and pulse shape
reported from Ginga data, and the pulsator continues to spin down. We
use our high spectral resolution data to search for cyclotron lines in
the spectrum that were claimed from observations made with other sate
llites. W, find that the ASCA spectra of 1E 2259+586 cannot be satisfa
ctorily fitted with either a single power law or a combination of two
power laws, and that significant residuals occur around 1.5 and 5 keV.
However, a combination of a power law and a blackbody gives a good fi
t over the entire ASCA energy band with no evidence of spectral featur
es. We have reanalyzed a Ginga LAC spectrum and find that this is also
significantly better fitted by this two-component spectrum than a sin
gle power law. A possible explanation for such a two-component spectru
m is that the blackbody emission comes from a neutron star and that th
e power-law component comes, at least in part, from a surrounding nebu
la. As there has, so far, been no direct evidence that 1E 2259+586 is
a binary system we consider whether there are other plausible mechanis
ms that might power the observed X-ray emission.