We have investigated the temperature and magnetic field dependencies of resistance of single crystal topological insulator Bi0.83Sb0.17 nanowires. Nanowire samples with diameters ranging from 75 nm to 1.1 μm were fabricated by radio frequency casting in a glass capillary (Ulitovsky technique) [1]. Owing to the quantum size effect, the energy gap Eg with decreasing diameter of the nanowires d from 1100 nm down to 75 nm) increases as Eg μ 1/d (for diameter d = 1.1 μm and d = 75 nm, Eg = 21 and 45 meV, respectively). Surface states manifest themselves as decreasing resistivity at low temperatures. The Shubnikov-de Haas oscillations observed in Bi0.83Sb0.17 nanowires at T = 1.5 and 3 K demonstrate the existence of high mobility (μS=26,700–47,000 cm2V−1s−1) 2D carriers in the surface areas of the nanowires, which are nearly perpendicular to the C3 axis. From the linear dependence of nanowire conductance on nanowire diameter at T = 4.2 K, we calculated the square resistance Rsq of the surface states of the nanowires to be only 70 Ohm [2]. In thin Bi0.83Sb0.17 nanowires (d ≤ 100 nm) at low temperatures (1.5 K ≤ T < 5 K), we discovered the Aharonov–Bohm (AB) oscillations of longitudinal magnetoresistance with two periods - one flux quantum, Φ0 and half of flux quantum, Φ0/2, (ΔB1 =Φ0/S, ΔB2 =Φ0/2S, where S is the cross-sectional area of the nanowire). The periods ΔB depend on the inclination angle α of the magnetic field direction according to the law ΔB=ΔBparallel/cosα. This law is preserved up to angles of about 60 degrees. The nonmonotonic changes of magnetoresistance, which are equidistant in a direct magnetic field, were observed in transverse magnetic fields under conditions where the magnetic flux through the cylinder Φ = 0. Possible reasons for this behavior by analogy with thin bismuth nanowires are discussed.