A device for cleaning the teats of the udder of a dairy animal. The device is provided with a cleaning member that is drivable by a drive member. The device is further provided with a power measuring system for measuring the power of the drive member during the drive of the cleaning member. A comparator compares the momentary value of the power measured by the power measuring system with a lower threshold. The comparator supplies a signal when the lower threshold is exceeded. A method of cleaning the teats of the udder of a dairy animal. The cleaning is carried out by a cleaning member driven by a drive member. The method comprises the steps of measuring the power of the drive member, of comparing the measured power with a power threshold value, of choosing a lower threshold as a power threshold value, and of supplying a signal when the lower threshold is exceeded.