Electromagnetic fields (EMFs) having strengths typically found in the general environment can alter brain activity, but the reported effects have been inconsistent. We theorized that the problem arose from the use of linear methods for analyzing what were actually nonlinear phenomena, and therefore studied whether the nonlinear signal-processing technique known as recurrence quantification analysis (RQA) could be employed as the basis of a reliable method for demonstrating consistent changes in brain activity. Our primary purpose was to develop such a method for observing the occurrence of evoked potentials in individual subjects exposed to magnetic fields (2G, 30 and 60 Hz). After all conditions that affected the analysis of the EEG were specified in advance, we detected magnetosensory evoked potentials (MEPs) in all 15 subjects (P<0.05 in each experiment). The MEPs, which occurred within the predicted latency interval of 109-504 ms, were independent of the frequency and the direction of the field, and were not detected using the traditional linear method of analysis, time averaging. When the results obtained within subjects were averaged across subjects, the evoked potentials could not be detected, indicating how real nonlinear phenomena can be averaged away when the incorrect method of analysis is used. Recurrence quantification analysis, but not linear analysis, permitted consistent demonstration of MEPs. The use of nonlinear analysis might also resolve apparent inconsistencies in other kinds of brain studies.