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It is proposed that the observed differences between odd and even solar cycles are a consequence of the nonlinear interactions that provide the stabilizing mechanism for the cycle's amplitude. If, for example, the magnetic field is larger than average for a given cycle (say odd), the nonlinear feedback mechanism can generate a magnetic field that is smaller than average for the next cycle (even), and then one that is larger than average for the following cycle (odd), etc. As a consequence the odd cycles have larger amplitudes than even cycles. A very simply model having a nonlinear interaction that reproduces this behavior is discussed.