A process for purifying exhaust air from a granulation plant for producing a urea-containing granulate includes contacting a gas stream containing a urea-containing dust and ammonia with a sulfuric acid solution or a nitric acid solution in a scrubbing process. The scrubbing process involves scrubbing the gas stream with a first weakly acidic scrubbing solution in a first scrubbing stage and scrubbing the gas stream exiting the first scrubbing stage with a second scrubbing solution having a lower pH than the first weakly acidic scrubbing solution in a second scrubbing stage. The acidic scrubbing solution generated in the second scrubbing stage may be recycled into the first scrubbing stage via a conduit and used therein as the first weakly acidic scrubbing solution. A pre-scrubbing stage for scrubbing dust out of the gas stream may additionally be arranged upstream of the first scrubbing stage.