  We consider a one dimensional elastic string as a set of massless beads
interacting through springs characterized by anisotropic elastic constants. The
string, driven by an external force, moves in a medium with quenched disorder.
We present evidence that the consideration of longitudinal fluctuations leads
to nonlinear behavior in the equation of motion which is {\it kinematically}
generated by the motion of the string. The strength of the nonlinear effects
depends on the anisotropy of the medium and the distance from the depinning
transition. On the other hand the consideration of restricted solid on solid
conditions imposed to the growth of the string leads to a nonlinear term in the
equation of motion with a {\it diverging} coefficient at the depinning
transition.
