Therefore, exchange-induced cross-peaks appear with frequencies (ω A , ω B ) and (ω B , ω A ), as demonstrated experimentally above (Fig. ). Having established a conceptual basis for these unexpected exchange cross-peaks, we sought to fit the observed spectra quantitatively, in order to verify our understanding of the process and to characterise the kinetics of the underlying exchange process. 2D lineshape fitting was performed using TITAN (which in this case reduces to the numerical integration of Eq. 1), and fits of NOESY spectra with both zero and non-zero mixing times reproduced the observed spectra very closely (Fig. ), with fitted exchange rates (indicated in the figures) consistent with published results. We also investigated the occurrence of exchange cross-peaks in other simple NMR experiments, and found that cross-peaks were also formed in COSY experiments, with a relative intensity of ca. 10% of the diagonal peaks (Fig. ). The precise form of these cross-peaks was different from those observed in the NOESY experiment (Fig. ), which reflects differences in the transfer of magnetisation between t 1 and t 2 evolution periods between the two pulse sequences, but again, high quality fits and measurement of the exchange rate could be obtained by 2D lineshape analysis (Fig. ).