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Bunching electrons by means of nonsinusoidal modulation is considered for linear electron beam devices including microwave klystrons and free electron lasers. A simple analytical formulation is developed to study the electron bunching in a nonsinusoidal bunching field for low power devices where space charge effects are not important. It is found that in general the current of the bunched electron beam depends on the derivative of the bunching field rather than the bunching field itself. This finding bears some important new implications for the consequent performance of electron beam devices. The analytical formulation is then verified with a numerical simulation. Space charge effects are also considered as a modification to the new formulation which leads to interesting insights to electron bunching with nonsinusoidal modulation.