A diagnostic system, for a valve (2), having a sensor (12) that senses structure-borne noise and having a device (14) for evaluating a measurement signal (13) of the structure-borne noise. During a calibration process, a first progression of the measurement signal is sensed for the closed position of the valve (2) and a first value (w1) of a characteristic is determined. To simulate leakage noise, the valve (2) is nearly closed during operation, a second progression of the measurement signal is sensed and a second value (w2) is determined. If the deviation of the second value from the first value is sufficiently large, a diagnosis is possible. A third progression of the measurement signal is sensed for the closed position of the valve as in an installed condition, and a third value (w3) is determined. If the deviation of the third value (w3) from the first value (w1) is too great, and if a diagnosis has been identified as being possible, then the system deduces that the valve leaks.