1. We have previously shown that steady-state coronary flow during auto-regulation and metabolic rate changes is predicted by a mathematically expressed theory which assigns control of coronary vascular resistance to tissue PO2. Our present purpose was to test the applicability of this theory to the non-steady state as exemplified by a sudden step change in heart rate. 2. The theory predicted that the response time of change of resistance in these circumstances would be slower with constant-flow perfusion of the coronary bed than with constant-pressure perfusion, and that with constant-pressure perfusion only, the rate of adaption of resistance would be dependent on the level of pressure used. 3. These predictions were tested in open-chest goats with cannulation of the left main coronary artery and perfusion with alternately constant pressure or constant flow. Sudden step changes in heart rate were induced by pacing to induce rapid transients in myocardial metabolic rate. 4. The half-time of subsequent change in perfusion pressure-flow ratio, which in the dynamical state is not equal to resistance, was 15.7 +/- 0.4 s (mean +/- S.E.M.), which was statistically shorter than for constant flow (22.2 +/- 0.5 s, P less than 0.001). 5. The half-time of subsequent change in perfusion pressure-flow ratio with constant-pressure perfusion was 14.4 +/- 0.6 s at low pressure and 17.0 +/- 0.6 s at high pressure (P less than 0.001). 6. The results differed from those predicted by the theory, in that the changes described above were preceded by a rapid (5 s) step change in pressure-flow ratio, up with an increase in heart rate and down with a decrease in heart rate. We postulated that this was a mechanical effect due to greater compression of the coronary microvasculature with more frequent contractions. 7. To test this hypothesis, we measured changes in coronary blood volume by integrating the difference between arterial inflow and venous outflow. These experiments showed a decrease in coronary blood volume with heart rate increase and vice versa. 8. Abolition of autoregulation and metabolic regulation was achieved with maximum vasodilatation of the coronary bed with adenosine. A sudden switch in heart rate then produced the initial step change in pressure-flow ratio, but not the subsequent adaptation over 13-25 s. This confirmed that the former effect is attributable to a passive mechanical mechanism.