Catch-and-release fisheries have become very important in the management of overexploited recreational fish stocks. Tag return studies, where the tag is removed regardless of fish disposition, have been used to assess the effectiveness of restoration efforts for these fisheries. We extend the instantaneous rate formulation of tag return models to allow for catch and release as well as harvest. The key point of our methods is that, given an estimate of the tag reporting rate, the fishing mortality rate (F) is separated into two components: the mortality on harvested fish and the "mortality" on tags (because the lags are removed) of fish released alive. The total fishing mortality rate for untagged fish is the sum of the Fs due to harvest and hooking mortality suffered by fish released alive. Natural mortality rates can also be estimated. Both age-independent models and age-dependent models are constructed, and the age-dependent models are illustrated by application to data from a study of striped bass Morone saxatilis in Chesapeake Bay from 1991 to 2003 by the Maryland Department of Natural Resources. By fitting models of the natural mortality rate with limited age and year dependence, we demonstrate an overall decrease in natural mortality rates as fish age and provide evidence of an increase in natural mortality beginning in the late 1990s, when an outbreak of the disease mycobacteriosis is thought to have begun. Our results indicate that fishing mortality is age dependent; selectivity increases up to age 6, when fish appear to be fully recruited to the fishery. There is also evidence of an increase in fishing mortality since 1995, when regulations were relaxed. ?? Copyright by the American Fisheries Society 2007.