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We provide a multiparameter analysis of dynamics in a nonautonomous system of two alternately exciting self-oscillatory elements that are able to demonstrate a uniformly chaotic attractor of Smale–Williams type in the stroboscopic Poincaré map. Parameter space charts of regular and chaotic regimes are presented. Possible scenarios of the onset of hyperbolic chaos are discussed. The numerical studies are supplemented by experimental results obtained for a laboratory electronic device.