  We set up a unified framework to efficiently compute the shear and bulk
viscosities of strongly coupled gauge theories with gravitational holographic
duals involving higher derivative corrections. We consider both Weyl$^4$
corrections, encoding the finite 't Hooft coupling corrections of the boundary
theory, and Riemann$^2$ corrections, responsible for non-equal central charges
$c\ne a$ of the theory at the ultraviolet fixed point. Our expressions for the
viscosities in higher derivative holographic models are extracted from a
radially conserved current and depend only on the horizon data.
