1. We tested predictions of a mathematical formulation of a hypothesis of dynamic control of coronary blood flow by tissue oxygen tension. 2. The rate of change of adjustment of the coronary circulation to a step change in arterial perfusion was analysed in the cannulated main stem preparation of the anaesthetized goat. The variable studied was the ratio between driving pressure and coronary flow, each averaged per heart beat. The response of this ratio was measured following a sudden change in perfusion pressure with constant‐pressure perfusion and a sudden change in flow with constant‐flow perfusion. 3. The rate of change of the pressure‐flow ratio was quantified by t50, the time required to establish half of the completed response. For a pressure decrease t50 was 4.9 +/‐ 0.2 s (n = 35) (mean +/‐ S.E.M., n = number of individual measurements), 11.3 +/‐ 1.2 s (n = 25) for a flow decrease, 14.5 +/‐ 1.6 (n = 34) for a pressure increase and 25.1 +/‐ 2.3 (n = 19) for a flow increase. 4. No effect of the level of flow or pressure on t50 was found for a decrease in perfusion. Furthermore, with a flow increase, the t50 value did not depend on the level of flow, which is in agreement with the outcome of earlier experiments where the response to a change in heart rate was measured. With a pressure increase, the mean t50 value of the pressure‐flow ratio was lower at high perfusion pressure but the difference with low perfusion pressure was not significant (P = 0.11). 5. The t50 value in the cases of an increase in pressure and flow are similar to those found for a change of heart rate in an earlier study. 6. Unlike step changes of metabolic rate, some of the measured responses to mechanical step changes were not predicted by the oxygen hypothesis. It is suggested that the increased rate of coronary adjustment induced by the reduction of coronary perfusion is due to arteriolar smooth muscle mechanics which apparently differ in strength depending on the direction of change of the arteriolar dimensions. 7. This suggestion is strengthened by the results of experiments in which smooth muscle responses were abolished with adenosine.