  We present results of long-term timing of eclipsing binaries PSR B1744-24A
and PSR B1957+20 at Arecibo, the VLA, and Green Bank. Both pulsars exhibit
irregularities in pulsar rotation and orbital motion. Increases and decreases
of the orbital period of PSR B1957+20 are of order Delta-P_b/P_b ~ 10^-7,
varying on a time scale of a few years. Over a decade of observations, the
orbital period of PSR B1744-24A has only decreased, with time scale
|P_b/P_b-dot| ~ 200 Myr. When the effects of orbital motion are removed from
the timing data, long-term trends remain in the pulse phase residuals, with
amplitudes of order 30 and 500 us, respectively, for B1957+20 and B1744-24A.
Such large "timing noise" is not seen in other spun-up pulsars (isolated or
binary), leading us to conclude that it is a consequence of mass flow in the
system. Possible causes include variations in the rotation of the pulsars and
movement of the binary systems along the line of sight (perhaps due to
gravitational interactions with outflowing matter).
