  In this paper, we derive a sub-gradient estimate for pseudoharmonic maps from
noncompact complete Sasakian manifolds which satisfy CR sub-Laplace comparison
property, to simply-connected Riemannian manifolds with nonpositive sectional
curvature. As its application, we obtain some Liouville theorems for
pseudoharmonic maps. In the Appendix, we modify the method and apply it to
harmonic maps from noncompact complete Sasakian manifolds.
