Abstract: In this paper, first the geometrical factor is derived and the integrodifferential equation of the instantaneous current and the beam kinetic energy in two-cavity klystrons is given. Then a nonlinear theory of cavity excitation by modulated electron beam is applied to calculate the amplitude and the phase of the gap voltage of the middle cavity, the relativistic error of the amplitude is 0.07%, the error of the phase is 2.15°. The coupling coefficient of the gap of the coaxial cavity is obtained. With electron beam voltage of 715.2 kV, electron beam current of 8 kA, and the gap voltages of the input cavity and the middle cavity of 14 kV and 315.2 kV respectively, the fundamental harmonic current modulation coefficient versus distance z is calculated by both the two dimensional particle in cell (PIC) simulation and the code of nonlinear theory. The results of the theory and the simulation agree remarkably well. With the beam propagation distance of 60.8 cm, the fundamental harmonic current modulation coefficient and the kinetic versus the normalized time are calculated, the normalization constant and the nth harmonic current modulation coefficient versus distance z are also calculated.