The conditions of mechanical equilibrium were considered, and the generalized notion of the surface tension at an arbitrarily curved surface layer was analyzed on the basis of the total nondiagonal pressure tensor including the external fields and anisotropic even in the bulk phases. It was shown that the transverse surface tension can be eliminated using the selection of a dividing surface; however, in the general case, this surface does not exhibit the properties of the tension surface. On the whole, three-dimensional and nondiagonal character of the tensors of excess surface stresses determined by the integration over the volume and the cross section of the surface layer is retained at any selection of the dividing surface.