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We consider the problem of embedding odometers in one-dimensional cellular automata. We show that (1) every odometer can be embedded in a gliders-with-reflecting-walls cellular automaton, which one depending on the odometer, and (2) an odometer can be embedded in a cellular automaton with local rule $x_i\mapsto x_i+x_{i+1}modn$ (i ∈ ℤ), where n depends on the odometer, if and only if it is “finitary.”