The torsional oscillations of seven single sunspots were investigated on observations of longitudinal magnetic field and velocities field in the photospheric line Fe I λ 525.3 nm. The periods of umbra and penumbra oscillations were 2.2—7.1 and 3.3—7.7 days, respectively. The sunspots at a greater solar latitude show a longer period of oscillations and smaller axial strength of magnetic field. The period and amplitude of the penumbra oscillations increase with the growth of period and amplitude of the sunspot umbra oscillations. The obtained results can be an evidence for the unitary mechanism of the torsional oscillations of umbra and penumbra of single sunspots and the connection of these oscillations with the differential rotation of the Sun.