M. Department of Computational Mathematics of the USSR Academy of Sciences, 1983. — 206 s . The results of the author's research on the theory and problems of numerical solution of problems on particle transfer. These results relate to variational principles in non-stationary energy-dependent problems, formulation of existence theorems based on these principles , the study of the smoothness of problems in the spaces of functions with differential-difference characteristics , problems of continuation of solutions with maintaining smoothness class , the problem of substantiating a number of approximate algorithms for solving the problems under real limitations on the source data. The results outlined in the book are new and of interest to both particle transfer problem theorists and to individuals researching the problems of constructing numerical solutions to these problems.