Pulse frequencies from the archival ROSAT observations of 1E 2259+586
are presented. A short-term spin-up episode superposed on the secular
spin-down trend is observed. Combining the previously published pulse
frequencies, we estimate the variance of the angular velocity over a 1
5 yr span of observations. The level of fluctuations in angular veloci
ty is similar to that of established accreting binary neutron stars. T
hese results favor accretion by a neutron star from a very low mass co
mpanion as the source of the X-ray luminosity, although accretion by a
solitary neutron star from a residual disk might be possible.