Abstract: Some Liouville theorems for F-stationary maps from some complete manifolds are obtained by assuming some conditions on the radial curvature, the degree of F(t) and the asymptotic behavior of the maps at infinity. In particular, the results can be applied to F-stationary maps from the Euclidean space (R^m, g₀) to a large class of Riemannian manifolds by assuming some conditions on the asymptotic behavior of the maps at infinity.