The kinematics, structure, and stellar population properties in the centers of two brightest early-type galaxies of the Leo II group, NGC 3607 and NGC 3608, are studied by means of integral-field spectroscopy. The kinematically distinct areas in the centers of these galaxies, with radii of 6 and 5 respectively, are found also to be chemically distinct. These stellar structures are characterized by enhanced magnesium-line strength in the integrated spectra. However, we have not found any mean stellar age differences between the decoupled cores and their outskirts. Analysis of the two-dimensional line-of-sight velocity fields reveals systematic turns of the kinematical major axes near the nuclei of both galaxies; in NGC 3608 the ionized gas rotates in the orthogonal plane with respect to the stellar component rotation. By taking into account some morphological features, we conclude that both NGC 3607 and NGC 3608 have large triaxial stellar spheroids. We argue that the magnesium-enhanced cores are not circumnuclear disks; instead they resemble rather compact triaxial structures which may be a cause of formation of polar disks around them - a gaseous one in NGC 3608 and a stellar-gaseous one in NGC 3607. In the latter galaxy the star formation is perhaps still proceeding over the polar disk.