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The official published version of this article can be found at the link below.The computing-intensive data mining for inherently Internet-wide distributed data, referred to as Distributed Data Mining (DDM), calls for the support of a powerful Grid with an effective scheduling framework. DDM often shares the computing paradigm of local processing and global synthesizing. It involves every phase of Data Mining (DM) processes, which makes the workflow of DDM very complex and can be modelled only by a Directed Acyclic Graph (DAG) with multiple data entries. Motivated by the need for a practical solution of the Grid scheduling problem for the DDM workflow, this paper proposes a novel two-phase scheduling framework, including External Scheduling and Internal Scheduling, on a two-level Grid architecture (InterGrid, IntraGrid). Currently a DM IntraGrid, named DMGCE (Data Mining Grid Computing Environment), has been developed with a dynamic scheduling framework for competitive DAGs in a heterogeneous computing environment. This system is implemented in an established Multi-Agent System (MAS) environment, in which the reuse of existing DM algorithms is achieved by encapsulating them into agents. Practical classification problems from oil well logging analysis are used to measure the system performance. The detailed experiment procedure and result analysis are also discussed in this paper