We have derived the largest class of bounded linear time-invariant operators that preserve positivity of repeated monotone nonlinearities. It reduces conservativeness of integral quadratic constraint (IQC) stability analysis of systems having repeated monotone nonlinearities to the minimum possible. Utility of this characterization stems from the fact that such nonlinearities are typically encountered in stability analysis of anti windup schemes among other applications. We have also derived the time varying counterpart of this class of operators.