A re there cycles in American politics? In particular, does the proportion of the Democratic/Republican vote share for president and/or seat share in Congress rise and fall over extended periods of time? If so, are the cycles regular, and what are the cycling periods? Moreover, if there are regular cycles, can we construct an integrated model--such as a negative feedback loop--that identifies political forces that could generate the observed patterns? First, we use spectral analysis to test for the presence and length of cycles, and show that regular cycles do, in fact, exist--with periods that conform to those predicted by the Schlesingers--for swings between liberalism and conservatism--but with durations much shorter than those most commonly claimed by Burnham and others in characterizing American political realignments. Second, we offer a voter--party interaction model that depends on the tensions between parties' policy and office motivations and between voters' tendency to sustain incumbents while reacting against extreme policies. We find a plausible fit between the regular cycling that this model projects and the time series of two-party politics in America over the past century and a half.