  We calculate the c-axis infrared conductivity $\sigma_c(\omega)$ in
underdoped cuprate superconductors for spinfluctuation exchange scattering
within the CuO$_2$-planes including a phenomenological d-wave pseudogap of
amplitude $E_g$. For temperatures decreasing below a temperature $T^* \sim
E_g/2$, a gap for $\omega < 2E_g$ develops in $\sigma_c(\omega)$ in the
incoherent (diffuse) transmission limit. The resistivity shows 'semiconducting'
behavior, i.e. it increases for low temperatures above the constant behavior
for $E_g=0$. We find that the pseudogap structure in the in-plane optical
conductivity is about twice as big as in the interplane conductivity
$\sigma_c(\omega)$, in qualitative agreement with experiment. This is a
consequence of the fact that the spinfluctuation exchange interaction is
suppressed at low frequencies as a result of the opening of the pseudogap.
While the c-axis conductivity in the underdoped regime is described best by
incoherent transmission, in the overdoped regime coherent conductance gives a
better description.
