The Teager-Kaiser operator is a discrete version of Teager's energy operator, advanced about 16 years ago. It is a filter of the moving window type and is commonly used as an estimator of the local energy contents of a signal; it is also used as a contrast enhancer of gray level images. We state some properties of a 2D version of the operator and its responses to common images. We characterize some of its root and preconstant images, and consider the case of separable images.