Abstract: A blood pumping system with a non-occlusive blood pump has a backflow warning generator to generate a warning to indicate that undesirable backflow of blood through the non-occlusive blood pump may be impending. The backflow warning generator comprises a microprocessor that executes a backflow alert routine that generates a backflow warning when one of two sets of conditions is satisfied. The first set of conditions tests for the presence of an average blood flow change rate within predetermined limits, an average blood flow within predetermined limits, and a change in the operating speed of the non-occlusive pump. the second set of conditions tests for the presence of an average blood flow greater than zero, a previous RPM value greater than a specified constant, and a current RPM value less than the specified constant.