In this article we represent results of theoretical investigations of transportation of high-current relativistic electron beam (HREB) in planar and coaxial drift-chambers, which are placed in the homogenous leading magnetic field. The limit currents are determined by solving the self-consistent nonlinear system of equations. The space pulsing of ribbon HREB in a planar drift-chamber is investigated in approximation of envelopes. The conditions of optimal transportation of annular beam in coaxial drift-chamber are developed. The dynamic of propagation of HREB in coaxial drift-chamber is considered by numerical methods. The computation of two-dimensional space structure of magnetic field of coaxial magnetic ondulator (CMO) is executed. The transportation of annual HREB in CMO is investigated. In approximation of envelopes the form of annular HREB in CMO is determined during it propagation by numerical methods.