We report here the observation of Aharonov-Bohm (AB) oscillations for single-crystal Bi nanowires with diameter d < 80 nm. [1] The nanowire samples with glass coating were prepared by the Ulitovsky technique; they were cylindrical single crystals with (1011) orientation along the wire axis. The surface of Bi nanowire supports surface states which give rise to a significant population of charge carriers with high effective mass that form a highly conducting tube around the nanowire. The oscillations of longitudinal magnetoresistance (MR) of Bi nanowires with two periods ΔB1 and ΔB2 proportional to Φ0 and Φ0/2 were observed, where Φ0 = h/e is the flux quantum. From B = 8 T down to B = 0 the extremums of Φ0/2 oscillations are shifted up to 3π at B = 0 which is the manifestation of Berry phase shift due to electron moving in a nonuniform magnetic field. The observed angle variation of the periods is not in agreement with the theoretical dependence Δ(α) = Δ(0)/cosα of the size effect oscillations of the flux quantization type. We have observed the non monotonic changes of transverse MR that are equidistant in the direct magnetic field. The period of oscillations depends on the wire diameter d as for the case of longitudinal MR. For 60 nm nanowire the period ΔB is equal to 1.54 T, but for 45 nm nanowire ΔB=1.88 T. Surprisingly, the period of oscillations in a wide range of angles (~50o) keeps constant value. The derivatives of transverse MR for two 45 nm bismuth nanowires were measured at various rotational angles of magnetic fields relative to nanowire C3 axis. Figure (left) shows the dependence of the Fast Fourier Transform (FFT) spectra of transverse MR for a 45 nm Bi nanowire on the angle θ between the direction of applied magnetic field B and the C3 wire axis. The observed angle variations of the amplitude of FFT spectra for two 45 nm nanowires are shown in Figure (right). At angles θ > 50o the non monotonic changes of transverse MR lose its periodicity on a direct magnetic field. The ARPES measurements show that the penetration length of Bi surface states is very anisotropic. The (100) surface supports deeply penetrating states, in contrast to trigonal surfaces, where the surface states are shallow. In 30 nm array of trigonal Bi nanowires the surface states occupy the whole volume of nanowires. [2] If the surfaces are, in fact, a combination of different single-crystal surfaces (as in our (1011) nanowires), one would expect the highly conducting area to be comparable with a tube with variable thickness (see sketch on figure). In multiwall carbon nanotubes, the observed h/e oscillations were attributed to the structure of the two-dimensional density of states. Considering the similarities between the Bi surface state tubes and carbon nanotubes, we propose an interpretation of the observed h/e oscillations of MR in terms of oscillations in the density of surface states. The h/2e oscillations arise due to Al’tshuler-AronovSpivak effect on surface states.