The gas-phase reaction between H ₂ and O ₂ is the prototype combustion reaction and one of the most studied chemical reactions. Previous work has reported the existence of sustained oscillatory ignition in open reactors driven primarily by chemical feedback (chain branching and self-inhibition) and of complex (mixed-mode) oscillations originating from the coupling of chemical and thermal feedback mechanisms. In this paper, additional complex responses are described for experiments with ‘fuel-rich’ mixtures at short residence times. Evidence for the existence of deterministic chaos in this system is presented. Almost all of the new complex behaviour can be modelled, at least semi-quantitatively, using the ‘minimal complex oscillator model’ comprising 12 elementary steps presented previously using kinetic data obtained from independent sources.