A new high-resolution indecomposable quasi-characteristics scheme with monotone properties based on pyramidal stencil is considered. This scheme is based on consideration of two high-resolution numerical schemes approximated governing equations on the pyramidal stencil with different kinds of dispersion terms approximation. Two numerical solutions obtained by these schemes are analyzed, and the final solution is chosen according to the special criterion to provide the monotone properties in regions where discontinuities of solutions could arise. This technique allows to construct the high-order monotone solutions and keeps both the monotone properties and the high-order approximation in regions with discontinuities of solutions. The selection criterion has a local character suitable for parallel computation. Application of the proposed technique to the solution of the time-dependent 2D two-phase flows through the porous media with the essentially heterogeneous properties is considered, and some numerical results are presented. (C) 2002 John Wiley & Sons, Inc.