We present the results of studying the passband properties of gyroklystrons theoretically and experimentally and analyze the main causes of limitations in the bandwidth of the frequencies that they amplify. It is shown that in the range of low beam currents, where the electron velocity spread is rather low, the amplification bandwidth of a two-cavity gyroklystron is close to the bandwidth of the output cavity loaded with an electron beam. In the range of high currents, the amplification bandwidth depends only weakly on the parameters of the output cavity and is determined mainly by the spread in the times of electron passing through the drift space, which is caused by the difference in their translational velocities. Good qualitative agreement of the calculated and experimental dependences indicates that the proposed method can be applied to the calculation and interpretation of frequency characteristics of gyroklystrons. The possibility to expand the passband of operating frequencies in the high-current region by decreasing the influence of the electron velocity spread on beam bunching in the three-cavity gyroklystron operating in the maximum acceleration regime is demonstrated experimentally. Theoretically, the developed method for calculation of frequency characteristics can be expanded to the case of a three-cavity gyroamplifier with slight modifications.