A detailed computer model of human erythrocyte metabolism was shown to predict three steady states, two stable and one unstable. The most extreme steady state is characterized by almost zero concentrations of all the phosphorylated intermediates. The "normal" steady state is remarkably robust in the face of large changes in the activity of most of the enzymes of glycolysis and the pentose phosphate pathway: this steady state can be viewed as an attractor towards which the system returns following a metabolic perturbation. Focus is given to three responses of the system: (1) the 'energy charge' that pertains to the concentration of ATP relative to all purine nucleotides; (2) redox power expressed as the ratio of reduced-to-total glutathione and (3) the concentration of 2,3-bisphosphoglycerate, that directly affects the oxygen affinity of haemoglobin thus affecting the main physiological function of the cell. The collapse of the normal steady state in what can be viewed topologically as a catastrophe is posited as one key element of erythrocyte senescence and it is particularly important for erythrocyte destruction in patients with an inborn enzyme deficiency.