Necessery and suf ficient conditions of unanimously reversibility of the nonlinear dif ference operators $(R_kx) = x(n+1) + (-1)^k f(x(n)), n ∈ \mathbb{Z}, k = \overline {1, 2}$, in the space of bounded two-sided number sequences are obtained. Here $f: \mathbb{R} → \mathbb{R}$ is a continuous function

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