The present invention relates to the field of regulating and presetting pump rates of blood pumps. It is directed at a device and a method in which the blood pressures are monitored upstream and/or downstream from the blood pump, and these values or another value formed from these values are compared with a limit value, which depends on an operating parameter or a pump parameter on the blood pump. In violation of the limit value, the pump rate of the blood pump is modified to such an extent or a new pump rate is determined so that the limit value is no longer violated or the degree of violation is reduced.