In this paper, the (blind) identifiability of systems using the second-order output cyclic spectra is considered. It is shown that the class of minimal, stable, rational causal (MSRC) systems is not identifiable, and the identification is limited by a nontrivial ambiguity associated with the so-called cyclic all-pass factor. The largest subclass of MSRC systems that ensures the unique identification is shown to be the set of MSRC systems that do not have special uniformly spaced maximum phase zeros.