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Discovered in 1907, the Blazhko effect is a modulation of the light variations of about half of the RR Lyr stars. It has remained unexplained for over 100 years, despite more than a dozen proposed explanations. Today it represents an ongoing challenge in variable-star research. We propose a new explanation. It is based on the observation that Blazhko stars seem to be located in the region of the instability strip where fundamental and first overtone modes are excited at the same time. The combined effects of these two shocks on the atmosphere cause the Blazhko effect. This effect can only exist if the first overtone mode is excited together with the fundamental mode. Because the involved physical mechanisms are essentially nonlinear (shocks, atmospheric dynamics, radiative losses, mode excitations), the Blazhko process is expected to be unstable and irregular. Consequently, the Blazhko process has a specific random nature that is in contrast with the pulsation of non-Blazhko stars.