Abstract. A second-order symmetric tensor over a three-dimensional Euclidean space is called non-degenerate if its eigenvalues differ one from another. In the paper a simple criterion for nondegeneracy is given, namely, it appears that the tensor is nondegenerate iff there exists a Cartesian system in which only one of the nondiagonal components of the tensor vanishes. As a consequence it is noticed that the eigenvalues of a symmetric 3 X 3 matrix are mutually different iff it is similar to a matrix which has only one vanishing nondiagonal element.