We investigate the extent of real convergence among G7 economies in terms of long-run real interest parity. A novel approach is applied where unit-root tests of real interest differentials are embedded within a Markov regime-switching framework. Whereas standard univariate unit-root tests provide little support for parity, we find real convergence is present after allowing for regime switches in real interest misalignments. However, differentials across members of the euro zone are likely to exhibit greater persistence despite nominal convergence. It is non-sequitur to infer from monetary unification that nominal convergence is necessarily conducive to real interest realignments or preventive of misalignments.