Acclimation by plants to hypoxia and anoxia is of importance in various ecological systems, and especially for roots in waterlogged soil. We present evidence for acclimation by roots via ‘anoxic’ cores rather than being triggered by O2 sensors. The evidence for ‘anoxic’ cores comes from radial O2 profiles across maize roots and associated metabolic changes such as increases in the ‘anaerobic enzymes’ ADH and PDC in the ‘anoxic’ core, and inhibition of Cl− transport to the xylem. These cores are predicted to develop within 15–20 min after sudden transfer of a root to hypoxia, so that the cores are ‘anoxically-shocked’. We suggest that ‘anoxic’ cores could emanate a signal(s), such as ACC the precursor of ethylene and/or propagation of a ‘Ca2+ wave’, to other tissue zones. There, the signalling would result in acclimation of the tissues to energy crisis metabolism. An O2 diffusion model for tissues with an ‘anoxic’ core, indicates that the phytoglobin-nitric oxide (Pgb-NO) cycle would only be engaged in a thin ‘shell’ (annulus) of tissue surrounding the ‘anoxic’ core, and so would only contribute small amounts of ATP on a whole organ basis (e.g. whole roots). A key feature within this annulus of tissue, where O2 is likely to be limiting, is that the ratio (ATP formed) / (O2 consumed) is 5–6, both when the NAD(P)H of glycolysis is converted to NAD(P)+ by the Pgb-NO cycle or by the TCA cycle linked to the electron transport chain. The main function of the Pgb-NO cycle may be the modulating of NO levels and O2 scavenging, thus preventing oxidative damage. We speculate that an ‘anoxic’ core in hypoxic plant organs may have a particularly high tolerance to anoxia because cells might receive a prolonged supply of carbohydrates and/or ATP from the regions still receiving sufficient O2 for oxidative phosphorylation. Severely hypoxic or ‘anoxic’ cores are well documented, but much research on responses of roots to hypoxia is still based on bulk tissue analyses. More research is needed on the interaction between ‘anoxic’ cores and tissues still receiving sufficient O2 for oxidative phosphorylation, both during a hypoxic exposure and during subsequent anoxia of the tissue/organ as a whole.