1. A pulmonary-bellows-ventilator system for controlling the breathing of an anesthetized and paralyzed patient undergoing surgery, comprising a pulmonary-bellows assembly having a housing, a bellows mounted within said housing forming a chamber therebetween, an inlet on said housing fluidically communicating with said chamber and an outlet means on said housing fluidically communicating with the interior of said bellows and for delivering gas to a patient said bellows having a maximum tidal volume, TV.sub.max, a constant-pressure driving-gas source; a switchable valve and an electrically controllable variable throttling valve, said valves connected in series from the output of said source to the input of said bellows assembly, said source and said throttling valve establishing together a maximum flow rate, F.sub.max, of said driving gas through said throttling valve; instruction input means for providing target values of the minute volume, MV, of driving gas delivered each minute from said source to said bellows assembly, the frequency, R, at which said switchable valve is opened and closed, the flow rate, F, of driving gas through said throttling valve during periods when said switchable valve is open, and the quantities F.sub.max and TV.sub.max, microprocessor means having inputs connected to said instruction input means for accepting and storing said target values, said microprocessor means having outputs connected to said switchable valve and said throttling valve, for establishing the actual frequency R, flow rate F and inspiration time I that corresponds to the time period during which said switchable valve is open, for determining the actual tidal volume TV and the ratio E/I of switchable-valve closed-time to open-time according to the relationships: ##EQU8## and when said target value MV.sub.T is larger than that MV value which corresponds to the combination of said target value for R and said maximum bellows tidal volume TV.sub.max, for changing said actual frequency R away from said target value R to a frequency R.sub.A corresponding to the combination of said TV.sub.max, and said MV target value, so that said target MV value is still actually realized according to ##EQU9##