This paper describes a stochastic dynamic programming based approach to solve Sensor Resource Management (SRM) problems such as occur in tracking multiple targets with electronically scanned, multi-mode radaz Specifically, it formulates the SRM problem as a stochastic scheduling problem and develops appmximate solutions based on the Gittins index rule. Novel results include a hybrid state stochastic model for the information dynamics of tracked targets, an exact index rule solution of the SRM problem for a simplified tracking model, and use of approximate dynamic pmgramming to extend the index rule solution to more realistic models.