The properties of the interatomic voids present in fully hydrated dimyristoylphosphatidyleholine (DMPC)cholesterol mixed membranes of different compositions are analyzed in detail using it generalized variant of the Voronoi-Delaunay method on the basis of computer simulation results. The systems investigated are chosen from both sides of the DMPC-cholesterol miscibility gap the pure DMPC bilayer has also been included in the analysis as a reference system. The results obtained show that the empty space is organized in a more compact way, forming larger voids in the presence than in the absence of cholesterol. The voids located in the region of the rigid cholesterol rings become. on average, less spherical, oriented more parallel with the membrane normal axis with increasing cholesterol concentration, whereas an opposite effect of cholesterol is observed in the middle of the membrane among the chain terminal methyl groups, In general, the preferential orientation of the voids is found to strongly correlate With that of the molecules in the hydrocarbon phase of the membranes. The membranes are found to contain rather large voids. the volume of which can be an order of magnitude larger than the largest spherical cavities present in the systems, These voids are elongated or branching channels rather than big empty holes, The voids located among the DMPC and cholesterol molecules are lying preferably parallel with the membrane normal axis, The existence of such empty channels can be of great importance in the cross-membrane permeation of small, uncharged penetrants, in particular, of polar molecules.