An important role of myoglobin in red muscle is to facilitate the diffusion of oxygen for metabolism. We consider a model for muscle respiration in which the oxygen consumption is of a Michaelis-Menten form. The resulting mathematical model is solved in two different ways with two different boundary conditions. The first uses the singular perturbation method of Murray (1974), while the second, which gives another justication of the simpler procedure, is a direct numerical computation of the full problem. The oxygen tension and saturation are often small. For realistic values of the Michaelis-MENTEN CONSTANT the oxygen tension, the saturation and the radius of the region in which the oxygen tension is negligibly small can be calculated using the constant consumption model of Murray (1974), with corrected boundary conditions (those for a Stefan problem), which in certain circumstances mardedly affect the solution.