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 th
ese observations, Aql X-1 passes through an apparent "propeller" II phase a
s 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 r
ms amplitude of any periodic signal contained in the various data sets sear
ched. This result has implications for the geometry of the system, if the q
uiescent luminosity is due to continued low-level accretion. Alternatively,
our result supports the idea that the quiescent luminosity may be due to t
hermal emission.