  Non-relativistic three-dimensional magnetohydrodynamic simulations of
Poynting-flux-dominated (PFD) jets are presented. Our study focuses on the
propagation of strongly magnetized hypersonic but sub-Alfv\'enic flow ($C_{\rm
s}^2 << V_{\rm jet}^2 < V_{\rm A}^2$) and the development of a current-driven
(CD) kink instability. This instability may be responsible for the "wiggled"
structures seen in VLBI-scale AGN jets. In the present paper we investigate the
nonlinear behavior of PFD jets in a variety of external ambient magnetized gas
distributions, including those with density, pressure, and temperature
gradients. Our numerical results show that PFD jets can develop kink
distortions in the trans-Alfv\'enic flow case, even when the flow itself is
still strongly magnetically dominated. In the nonlinear development of the
instability, a non-axisymmetric mode grows on time scales of order the Alfv\'en
crossing time (in the jet frame) and proceeds to disrupt the kinematic and
magnetic structure of the jet. Because of a large scale poloidal magnetic field
in the ambient medium, the growth of surface modes ({\it i.e.}, MHD
Kelvin-Helmholtz instabilities) is suppressed. The CD kink mode ($m = 1$) grows
faster than the other higher order modes ($m > 1$), driven in large part by the
radial component of the Lorentz force.
