We present the design and implementation of a general task monitoring and steering system for Grid applications (GSTAT). The system is integrated in the GRID superscalar (GRIDSs) programming framework. Information at the application, Grid node, and individual task levels are supplied upon request. Using the steering capabilities, individual tasks or the whole application can be cancelled. The corresponding jobs can be restarted using fault tolerance and checkpointing capabilities based on GRIDSs. In addition, the computational resources assigned to an application can be modified. GSTAT is tested using high throughput and high performance computing cases on an Internet-based Grid of computers.