In the work shows a way of developing the theory of nonlinear non-stationary two-beam traveling wave tube with a codirected beams, based on the nonlinear theory of traveling wave tube with a single electron beam. The need to build a double-beam traveling wave tube theory arose from the study of two-stream amplifier. It consists of an input device, an output device and the drift space, where two electron beams interact. In the input device there is a stream of modulation, which interact with each other in the drift space due to the phenomenon of two-stream instability. As input and output device of two-stream amplifier can be used spiral segments, so the input and output devices will be short section of double-stream traveling wave tube. Two-stream amplifier, due to lack of slow-wave system is a promising tool for advancement in terahertz region. The purpose of this work is to construct a theory of nonlinear nonstationary two-beam traveling wave tube with codirected beams. Currently, there are a lot of works about two-stream instability, much less work about a specific two-beam devices, none of them considers the time-dependent model. The resulting system was solved numerically by the method of particles in cells. A comparison of the test results of the theory with nonlinear equations of two-stream amplifier that showed the correctness of derived equations. The comparison operation TWT and two-stream amplifier in the non-stationary area of operating conditions and in the interference area. The comparison of two-stream amplifier in which the inlet and outlet sections of the device modeled TWT, with dual beam traveling wave tube of the same length.