Abstract A mathematical expression has been developed to describe the ventilatory responses to changes in arterial oxygen saturation (Sa O 2) and arterial carbon dioxide tension (P CO 2). The derivation is based on the experimental observations: (1) that ventilation is a linear function of P CO 2 under isoxic conditions, and (2) that ventilation is a linear function of Sa O 2, under isocapnic conditions. It is assumed that all functions are continuous and single valued, with the implication that for any given Sa O 2, and P co 2 there is a unique ventilatory response. The analysis following from these three assumptions has enabled us to derive the following expression for ventilation: Vi(Sa O 2, p co 2 = α 1·Sa CO 2·P CO 2+α 2·Sa O 2+α 3·P CO 2+α 4 where the α's are constants for an individual. This equation, which follows uniquely from the assumptions stated, is simpler and contains fewer parameters than previous expressions used to describe ventilation.