In present paper the processes of electron-wave interaction in the cathode driven crossed-field amplifiers are studied. These tubes have a higher gain due to the use of the weakly coupled delay lines placed on the anode and negative electrode (cathode). As a result the r.f. signal of same frequency is applied to the input of a cathode delay line (or to the inputs of the anode and cathode delay lines) and after an amplification the signal is coming to the output of the anode delay line (the mode of cathode excitation)