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We present a first study of the pulse line ion accelerator operating in a multipulse, multisection mode. The study is directed towards applications with long beam pulse in a long linac with a series of accelerating structures. We show that this operating mode is possible provided that the amplitude of the accelerating voltage waveform does not change over the entire pulse train and the operating frequencies of different sections are the same. A design criteria for the length and energy gain of a multisection linac is derived, and is applied to an example of a heavy ion linac injector.