We determine the model-independent component of the couplings of axions to electroweak gauge bosons, induced by the minimal coupling to QCD inherent to solving the strong CP problem. The case of the invisible QCD axion is developed first, and the impact on $W$ and $Z$ axion couplings is discussed. The analysis is extended next to the generic framework of heavy true axions and low axion scales, corresponding to scenarios with enlarged confining sector. The mass dependence of the coupling of heavy axions to photons, $W$ and $Z$ bosons is determined. Furthermore, we perform a two-coupling-at-a-time phenomenological study where the gluonic coupling together with individual gauge boson couplings are considered. In this way, the regions excluded by experimental data for the axion-$WW$, axion-$ZZ$ and axion-$Zgamma$ couplings are determined and analyzed together with the usual photonic ones. The phenomenological results apply as well to ALPs which have anomalous couplings to both QCD and the electroweak bosons.
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