The paper describes an approach to the parallel natural join execution on computing clusters with GPU and MIC Coprocessors. This approach is based on a decomposition of natural join relational operator using the column indices and domain-interval fragmentation. This decomposition admits parallel executing the resource-intensive relational operators without data transfers. All column index fragments are stored in main memory. To process the join of two relations, each pair of index fragments corresponding to particular domain interval is joined on a separate processor core. Described approach allows efficient parallel query processing for very large databases on modern computing cluster systems with many-core accelerators. A prototype of the DBMS coprocessor system was implemented using this technique. The results of computational experiments for GPU and Xeon Phi are presented. These results confirm the efficiency of proposed approach