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Knowledge has become increasingly important to support intelligent process automation and collaborative problem solving in large-scale science over the Internet. This paper addresses distributed knowledge management, its approach and methodology, in the context of Grid application. We start by analyzing the nature of Grid computing and its requirements for knowledge support; then, we discuss knowledge characteristics and the challenges for knowledge management on the Grid. A Semantic Web-based approach is proposed to tackle the six challenges of the knowledge lifecycle—namely, those of acquiring, modeling, retrieving, reusing, publishing, and maintaining knowledge. To facilitate the application of the approach, a systematic methodology is conceived and designed to provide a general implementation guideline. We use a real-world Grid application, the GEODISE project, as a case study in which the core Semantic Web technologies such as ontologies, semantic enrichment, and semantic reasoning are used for knowledge engineering and management. The case study has been fully implemented and deployed through which the evaluation and validation for the approach and methodology have been performed.