Among the newly discovered classes of X-ray sources which have attracted wide attention are close binary systems in which mass is transferred via Roche lobe overflow from a low mass donor star to its neutron star companion. Many of these sources exhibit intense bursts of X-ray radiation as well as periodic and quasi-periodic phenomena. Intensive analysis of these sources as a class has provided insight into the accretion process in binary star systems and into the magnetic field, rotational, and nuclear evolution of the underlying neutron star. In this proposal we have focused on theoretical studies of the hydrodynamical and nuclear processes that take place on the surface of accreting neutron stars in these systems. The investigation of these processes is critical for providing an understanding of a number of outstanding problems related to their transient behavior and evolution.
