We investigate the quantum mechanical process of two-electron tunneling in
strong external electric fields. Numerical solution of a two-electron s-wav
e model reveals: the existence of collective tunneling ionization in a mode
where both electrons stay at equal distance from the nucleus. Otherwise th
e lagging electron is immediately recaptured. The corresponding double ioni
zation rate fails to explain nonsequential multiple ionization in strong-fi
eld laser experiments. However, an empirically modified version of the anal
ytical one-electron tunneling rate of Ammosov, Delone, and Krainov agrees w
ith the experiments to a surprising accuracy. The reason for this agreement
is presently unknown.