  We show that various factors can lead to an isotopic dependence of the
penetration depth $\delta$. Non-adiabaticity (Jahn-Teller crossing) leads to
the isotope effect of the charge carrier concentration $n$ and, consequently,
of $\delta$ in doped superconductors such as the cuprates. A general equation
relating the isotope coefficients of $T_c$ and of $\delta$ is presented for
London superconductors. We further show that the presence of magnetic
impurities or a proximity contact also lead to an isotopic dependence of
$\delta$; the isotope coefficient turns out to be temperature dependent,
$\beta(T)$, in these cases. The existence of the isotope effect for the
penetration depth is predicted for conventional as well as for high-temperature
superconductors. Various experiments are proposed and/or discussed.
