The moveout approximations can be used in kinematic modeling, velocity analysis, and time migration. The generalized moveout approximation involves five approximation parameters and has several known approximations as special cases. A method is demonstrated for determining parameters of the generalized nonhyperbolic moveout approximation for qP- and qSV-waves in a homogeneous transversely isotropic medium with vertical symmetry axis (VTI medium). The additional parameters for the generalized approximation are computed from the hyperbolic asymptote at infinite offset. Comparison with a few well-known moveout approximations for higher-order terms in the Taylor series and asymptotic behavior shows that the generalized moveout approximation is superior to other nonhyperbolic approximations. A few numerical examples for qP- and qSV-waves in a VTI medium also indicate that the generalized approximation performs the best.