We investigate sinusoidal perturbations by an alternating electrical current imposed on focal steady states close to a Hopf bifurcation in the enzymatic peroxidase-oxidase (PO) and in the organic/inorganic Belousov-Zhabotinsky (BZ) reaction. Dynamic responses such as periodic, complex periodic, and chaotic resonances are observed. For low perturbation amplitudes both systems show period-1 resonances whereas for higher current perturbation amplitudes a period doubling route to chaos is found in the BZ reaction when the perturbation frequency is increased. Chaotic responses have also been found in the PO reaction when oxygen flow perturbations were applied to a focus. Model calculations using the Aguda-Larter PO model and the four-variable Gyorgyi-Field BZ model are in good agreement with the experiments.