A computer-controlled apparatus and method for perfusing a biological organ, such as a heart, kidney, liver, etc. The apparatus comprises a plurality of fluid reservoirs and an organ container for holding the biological organ. A first fluid flow path is defined as a loop from the plurality of reservoirs to necessary sensors and temperature conditioning means and back to the plurality of reservoirs. The reservoirs are selectively connectable to the first fluid flow path. Pump means are interposed in the first fluid flow path for pumping fluid from the first fluid flow path to a second fluid flow path. The organ container is located in this second fluid flow path. Pump means may also be included in the second fluid flow path for pumping fluid from the organ container to one or more of the reservoirs or to waste. One or more sensors are interposed in the fluid flow paths for sensing at least one of the concentration, temperature, pH, and pressure of the fluid flowing in the first and second fluid flow paths. Measuring means are interposed in the first and second fluid flow paths for measuring concentration and temperature differences between the upstream and downstream sides, in the fluid flow direction, of the organ container. The sensor(s) and the measuring means are connected to a programmable computer for providing a continuous information stream from the sensor(s) to the computer. The computer is coupled to the selection means and the pump means to continuously selectively control (a) the flow of fluid from each of the reservoirs individually to the fluid flow paths, and (b) at least one of the concentration, temperature, pressure and pH of the fluid flowing in the second fluid flow path, in accordance with a predetermined computer program without operator intervention.