The book summarizes the results of fundamental studies of gas dynamics of substance transfer in close binary stars that are at the mass exchange stage. The basic information about the physics of the processes of exchange of substances in close double systems. is given. The general principles of numerical modeling are considered and an overview of modern numerical methods most often used to solve gas-dynamic astrophysical problems is presented. The results of numerical modeling of gas dynamics of matter in close double systems without a magnetic field are presented . Changes in the pattern of currents caused by the presence of magnetic fields in close binary systems. The book is intended for researchers, graduate students and students of older courses studying in the specialty "Astrophysics" .