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The starspots on the surface of many chromospherically active binary stars concentrate on long-lived active longitudes separated by 180°. Shifts in activity between these two longitudes, the "flip-flop" events, have been observed in single stars like FK Comae and binary stars like σ Geminorum. Recently, interferometry has revealed that ellipticity may at least partly explain the flip-flop events in σ Geminorum. This idea was supported by the double-peaked shape of the long-term mean light curve of this star. Here we show that the long-term mean light curves of 14 chromospherically active binaries follow a general model that explains the connection between orbital motion, changes in starspot distribution, ellipticity, and flip-flop events. Surface differential rotation is probably weak in these stars, because the interference of two constant period waves may explain the observed light curve changes. These two constant periods are the active longitude period $({P}_{\mathrm{act}})$ and the orbital period $({P}_{\mathrm{orb}})$. We also show how to apply the same model to single stars, where only the value of Pact is known. Finally, we present a tentative interference hypothesis about the origin of magnetic fields in all spectral types of stars.