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We report the discovery of periodic modulation of pulsation in 51 fundamentalmode classical Cepheids of the Magellanic Clouds observed by the OpticalGravitational Lensing Experiment. Although the overall incidence rate is verylow, about 1 per cent in each of the Magellanic Clouds, in the case of the SMCand pulsation periods between 12 and 16d the incidence rate is nearly 40 percent. On the other hand, in the LMC the highest incidence rate is 5 per centfor pulsation periods between 8 and 14d, and the overall amplitude of theeffect is smaller. It indicates that the phenomenon is metallicity dependent.Typical modulation periods are between 70 and 300d. In nearly all stars themean brightness is modulated, which, in principle, may influence the use ofclassical Cepheids for distance determination. Fortunately, the modulation ofmean brightness does not exceed 0.01 mag in all but one star. Also, the effectaverages out in typical observations spanning a long time base. Consequently,the effect of modulation on the determination of the distance moduli isnegligible. The relative modulation amplitude of the fundamental mode is alsolow and, with one exception, it does not exceed 6 per cent. The origin of themodulation is unknown. We draw a hypothesis that the modulation is caused bythe 2:1 resonance between the fundamental mode and the second overtone thatshapes the famous Hertzsprung bump progression.

Unstable standard candles. Periodic light curve modulation in fundamental mode classical Cepheids