One of the key functionalities provided by Grid systems is the remote execution of applications. This paper introduces a research proposal on fault-tolerance mechanisms for the execution of sequential and message-passing parallel applications on the Grid. A service-based architecture called CPPC-G is proposed. The CPPC (Controller/Precompiler for Portable Checkpointing) framework is used to insert checkpointing instrumentation into the application code. CPPC-G services will be in charge of the submission and monitoring of the application execution, management of checkpoint files generated by CPPC-enabled applications, and detection and automatic restart of failed executions. The development of the CPPC-G architecture will involve research in different areas such as storage and management of data files (checkpoint files); automatic selection of suitable computing resources; reliable detection of execution failures and robustness issues to make the architecture fault-tolerant itself.