  We searched for coherent X-ray pulsations from Aql X-1 in a series of RXTE
observations taken shortly after a recent outburst. During the course of these
observations, Aql X-1 passes through an apparent ``propeller'' phase as its
luminosity fades to its quiescent value. No pulsations were detected, and we
place upper limits (ranging from 0.52% to 9.0%) on the fractional RMS amplitude
of any periodic signal contained in the various data sets searched. This result
has implications for the geometry of the system, if the quiescent luminosity is
due to continued low-level accretion. Alternatively, our result supports the
idea that the quiescent luminosity may be due to thermal emission.
