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The Grid supports the sharing and coordinated use of resources in dynamic heterogeneous distributed environments. The effective use of a Grid requires the definition of an approach to manage the heterogeneity of the involved resources that can include computers, data, network facilities and software tools provided by different organizations. This issue get more importance when complex applications, such as data-intensive simulations and data mining applications, executed on a Grid. This paper is concerned with heterogeneous resource management in Grid-based data mining applications. It discusses how resources are represented and managed in the KNOWLEDGE GRID and how XML-based metadata are used to describe data mining tools, data sources, mining models and execution plans, and how those metadata are used for the design and execution of distributed data mining applications on Grids.