  To gain insight into the out-of-plane electrodynamics of high-$T_c$
superconduct ors we have measured the absolute values and temperature
dependence of the c-a xis magnetic penetration depth $\lambda_c(T)$ for two
typical single layer high -$T_c$ cuprates, La$_{2-x}$Sr$_x$CuO$_4$ and
HgBa$_2$CuO$_{4+x}$ as a function o f doping. A distinct change in the
behaviour of $\lambda_c$ is observed near 0. 20 holes/Cu, which is related to
the opening of the normal state pseudogap. The variation of $\lambda_c$ with
doping is qualitatively similar to that of the in -plane component, $\lambda
_{ab}$, which suggests that the c-axis superfluid r esponse is mainly governed
by the superconducting condensation energy. The stron g doping dependence of
$\lambda_c(0)$ for p<0.20 provides an explanation for the discrepancies in the
literature.
