  I review the rotation measurements of accreting neutron stars. Many of the
highly magnetic accreting X-ray pulsars have been continuously observed with
the Burst and Transient Source Experiment (BATSE) aboard the Compton Gamma-Ray
Observatory (CGRO) since April 1991. These observations show that the accretion
torque exerted on many disk-fed accreting X-ray pulsars changes sign on a
monthly to yearly timescale. This results in alternating periods of spin-up and
spin-down with nearly the same torques, leading to little net angular momentum
gained by accretion. I also summarize recent discoveries with the Rossi X-Ray
Timing Explorer (RXTE) of periodicities during Type I X-ray bursts. These seem
to indicate that many of the rapidly accreting and weakly magnetic neutron
stars in our galaxy are rotating at frequencies greater than 250 Hertz. Most
remarkable is that they all rotate within a rather narrow range of frequencies.

Astrophysics