  It is well known that the standard transport equations violate causality when
gradients are large or when temporal variations are rapid. We derive a modified
set of transport equations that satisfy causality. These equations are obtained
from the underlying Boltzmann equation. We use a simple model for particle
collisions which enables us to derive moment equations non-perturbatively, i.e.
without making the usual assumption that the distribution function deviates
only slightly from its equilibrium value. We apply the model to two problems:
particle diffusion and viscous transport. In both cases we show that signals
propagate at a finite speed and therefore that the formalism obeys causality.
When the velocity gradient is large on the scale of a mean free path, the
viscous shear stress is suppressed relative to the prediction of the standard
diffusion approximation. The shear stress reaches a maximum at a finite value
of the shear amplitude and then decreases as the velocity gradient increases.
In the case of a steady Keplerian accretion disk with hydrodynamic turbulent
viscosity, the stress-limit translates to an upper bound on the Shakura-Sunyaev
$\alpha$-parameter, namely $\alpha<0.07$. The limit on $\alpha$ is much
stronger in narrow boundary layers where the velocity shear is larger than
Keplerian.
