  We present a theoretical quasiclassical study of the formation, during
Coulomb explosion, of two highly excited neutral H atoms (double H$^{*}$) of
strongly driven H$_2$. In this process, after the laser field is turned off
each electron occupies a Rydberg state of an H atom. We show that two-electron
effects are important in order to correctly account for double H$^{*}$
formation. We find that the route to forming two H$^{*}$ atoms is similar to
pathway B that was identified in Phys. Rev. A {\bf 85} 011402 (R) as one of the
two routes leading to single H$^{*}$ formation. However, instead of one
ionization step being "frustrated" as is the case for pathway B, both
ionization steps are "frustrated" in double H$^{*}$ formation. Moreover, we
compute the screened nuclear charge that drives the explosion of the nuclei
during double H$^{*}$ formation.
