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We have studied numerically one‐dimensional rf driven motion of domain structures. The equation of motion solved has Landau–Lifshitz damping and includes all the basic phenomenological magnetic interactions: demagnetizing field, anisotropy field, and exchange field. We have found that for a large range of parameters, the spatial average of the magnetization is chaotic in time, and the spatial pattern at fixed time itself is likewise chaotic. The power spectrum of the chaotic time series has a 1/f shape. The phase boundary between chaotic and nonchaotic motion is described, and a limited analytical insight into this problem is discussed.