  We study parabolic linear Weingarten surfaces in hyperbolic space
$\rlopezh^3$. In particular, we classify two family of parabolic surfaces:
surfaces with constant Gaussian curvature and surfaces that satisfy the
relation $a\kappa_1+b\kappa_2=c$, where $\kappa_i$ are the principal
curvatures, and $a,b$ and $c$ are constant.
