In this article we represent results of theoretical investigations of amplification of microwave in a coaxial ubitron, which undulator is made of permanent annular magnets. Undulator of such type are used both for focusing of high-current relativistic electron beam (REB) and for excitation of microwave radiation. The space structure of coaxial magnetic field of undulator is determined. We achieve that the specified conditions on parameters of coaxial undulator (tensity of magnetic field, period of undulator) have to be fulfilled for optimal transportation of REB. In coaxial undulator electrons of beam make periodical azimuth oscillations, which reduce to excitation of electromagnetic waves of TE-type. The linear theory of amplification of microwave in coaxial undulator is defined. The dependences of space increment on parameters of system (REB current, intensity of magnetic field of undulator) are obtained by solving of dispersion equation. The system of nonlinear equations, which describes nonlinear characteristics of ubitron (output power, efficiency), is determined for finding nonlinear characteristics of ubitron. The dependences of maximal efficiency of ubitron-ampifier on beam current and intensity of magnetic field are obtained as result of numerical analysis of nonlinear system of equation.