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This Report summarizes research activity within the framework of the research contract "Improvement of Streamline Simulation Technology (Altstream)" performed by research group at the Institute for Problems in Mechanics of the Russian Academy of Sciences during the period April 1, 2005- March 31, 2006. The objectives of the Project were to explore possibilities of advancing techniques of computer modelling of petroleum reservoirs on the basis of streamline simulator in combination with alternative mathematical models of the reservoir processes. Two directions of research were pursued, namely incorporation of the dual-porosity approach for two- and three-phase systems into FrontSim simulator, and further development and study of the alternative approach to compositional simulation of reservoir flows of multicomponent hydrocarbon mixtures.