Title: The Angular Momentum of Accreting Neutron Stars

Abstract: 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.