  We investigate the causality and stability of relativistic dissipative fluid
dynamics in the absence of conserved charges. We perform a linear stability
analysis in the rest frame of the fluid and find that the equations of
relativistic dissipative fluid dynamics are always stable. We then perform a
linear stability analysis in a Lorentz-boosted frame. Provided that the ratio
of the relaxation time for the shear stress tensor, $\tau_\pi$, to the sound
attenuation length, $\Gamma_s = 4\eta/3(\varepsilon+P)$, fulfills a certain
asymptotic causality condition, the equations of motion give rise to stable
solutions. Although the group velocity associated with perturbations may exceed
the velocity of light in a certain finite range of wavenumbers, we demonstrate
that this does not violate causality, as long as the asymptotic causality
condition is fulfilled. Finally, we compute the characteristic velocities and
show that they remain below the velocity of light if the ratio
$\tau_\pi/\Gamma_s$ fulfills the asymptotic causality condition.
