To clarify the physical nature of the orbital magnetic dipole excitations discussed widely in the past few years, a semiclassical model is presented and the nuclei a56Gd and 164Dy are investigated microscopically. The semiclassical model involves a consistent treatment of vibrational and rotational degrees of freedom; the microscopic results are obtained in quasiparticle-random-phase approximation (QRPA) with a realistic effective interaction. The results disagree with the picture of scissors modes or rotational vibrations.