Abstract: The paper is concerned with the methodology for speculative query execution support in distributed Relational Database Management Systems (RDBMS). The proposed approach is based on the analysis of the multi-graph representations of the stream of input queries arriving to a RDBMS. As a result, the optimized set of speculative queries is found to support current queries execution. The speculative query results are used to speed-up execution of the incoming query input stream. The considered RDBMS type assumes that the queries in the analysed input stream are of a similar type and concern information on products of a warehouse, specified according to standardized criteria. The paper presents how the proposed speculative query execution approach can be implemented inside a novel distributed program design framework PEGASUS DA in which program execution decisions are taken based on the system-supported monitoring of the distributed application global states. The paper shows the architecture of the speculative support provided by such framework for the distributed RDBMS and the assumed speculation approach. The implementation issues of the multi-threaded distributed support based on the RDBMS SQLite engines are discussed. Different approaches for executive system node roles are considered, concerning distributed data synchronization and speculative queries execution strategy as well as storing speculation results. The proposed approach to distributed implementation of the speculative support to RDBMSs using the PEGASUS DA framework is illustrated on the example of the modifying query handling in a RDBMS facing the presented speculative query support for query execution.