Abstract We considered the theoretical differences between the normal relationships of coronary blood flow and perfusion pressure in the working heart and those obtained with continuous, steady-flow perfusion by a roller pump during aortic valve replacement. Steady pump perfusion should deliver less blood flow to the endocardium because: 1. For the same mean artery perfusion pressure, the average coronary blood flow is less with constant-flow pump perfusion. 2. With constant pump perfusion, pressure would be excessively high during systole, and during diastole it would be significantly lower than the mean perfusion pressure. Instantaneous pressure and flow were measured in the left coronary artery in 8 patients undergoing aortic valve replacement, employing either roller pump perfusion or a gravity flow system to provide a steady pressure source. Although we did not attempt to demonstrate improved endocardial flow, the mean left coronary flow was always greater with gravity perfusion (297 versus 153 ml/min), lending support to the theoretically proposed differences between the two perfusion methods.