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The traveling‐wave amplifier is a typical structure where E‐M waves and electrons, traveling with approximately the same velocity, exhibit a strong interaction. The problem has usually been discussed for the case of weak waves with approximations corresponding to a small signal theory. It is interesting to state the limitations of this theory and to discuss the behavior of such tubes for strong signals. It seems that the amplified wave obtained in the case of small signals is progressively distorted until a final stage is reached where no further amplification is possible. The type of final distorted wave depends essentially upon all the details of the structure. In many cases where a complete investigation was possible, some strange types of shock waves were obtained, with a complete bunching of the space charge. A similar solution also applies to the linear accelerators or to the synchrotrons.