The azimuth moveout (AMO) operator in homogeneous, moderate to strong, anisotropic media, like in isotropic media, has an overall skew saddle shape. Yet, the AMO operator in anisotropic media is complicated; it includes, among other things, triplications at low angles. Even, in weaker anisotropies, with anisotropy parameter =0.1 ( anisotropy), the AMO operator differs from the isotropic one, though does not include triplications. The structure of the operator in VTI media (positive ) is stretched compared to operators in the isotropic media, with the amount of stretch dependent on the strength of anisotropy. If the medium is both v(z) and anisotropic, a likely combination in practical problems, the shape of the operator again differs from that for isotropic media. Yet, the difference in the AMO operator for the homogeneous case and the v(z) one is small even for anisotropic media. Simply stated, anisotropy impacts AMO more than typical smooth vertical velocity variations.