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This paper deals with the problem of recovering a band-limited process after it has been distorted by an instantaneous non-linearity and subsequently band-limited. Several uniqueness theorems for the input-output relationships are derived. In contrast with the deterministic case, no requirement that the nonlinearity be monotonic is made here. An iterative procedure for the recovery of the input is presented. Applications to two-level quantizers are considered, and a new result on the determination of a band-limited Gaussian process from its zero crossings is obtained.