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At the recent Second International Meeting on Brain-Computer Interfaces (BCIs) held in June 2002 in Rensselaerville, NY, a formal debate was held on the pros and cons of linear and nonlinear methods in BCI research. Specific examples applying EEG data sets to linear and nonlinear methods are given and an overview of the various pros and cons of each approach is summarized. Overall, it was agreed that simplicity is generally best and, therefore, the use of linear methods is recommended wherever possible. It was also agreed that nonlinear methods in some applications can provide better results, particularly with complex and/or other very large data sets.