An injector for the injection of a fluid into human or animal bodies with a pump for the conveying of the fluid at a flow rate, and with a control device for the control of the pump and for the setting of a desired flow rate (theoretical flow) of the fluid, and a pressure measurement device coupled with the control device for the recording of the pressure of the fluid conveyed by the pump, wherein a theoretical pressure is specified for the control device. In order, on the one hand, to reliably prevent an exceeding of a pressure hazard in the injection system and, on the other hand, to avoid an unnecessary prolongation of the injection process by a power reduction or a switching off of the drive mechanism, and to increase the throughput of several injection processes carried out with the injector one after the other, provision is made so that the control device compares the pressure of the fluid recorded by the pressure measurement device to the theoretical pressure, and when the theoretical pressure is exceeded over a time period, integrates the chronological pressure course of the pressure recorded by the pressure device over this time period for the determination of a pressure integral, and switches off the pump or operates it with a lower pump power if the determined pressure integral exceeds a prespecified integral limiting value.