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The effects of asymmetry atmospheric eddies on the beam spreading and wander of Bessel-Gaussian (BG) beams in anisotropic turbulence are studied. Results show that turbulence anisotropy leads to the declines in both beam spreading and wander of BG beams in the atmosphere. A BG beam with larger beam shape parameter η has a narrower spot size in a short-distance range and a wider spot size in a long-distance range. The effective Rayleigh ranges of BG beams for every turbulent situation decrease with the beam shape parameter η. When η is larger than 10, atmospheric turbulence has a negligible effect on effective Rayleigh range. The effective Rayleigh range and beam spreading increase and beam wander decreases as topological charge increase. Beam spreading is mainly affected by turbulence inner-scale, and outer-scale evidently affects beam wander in the atmosphere.