Rrcwcd 17 Seprcnrber I981 Mtli the excepIlon of a few early experiments (I-31, the hrgh Ionization potenkd of H, has not allowed derailed mulripholon smdles Recent advances III the generation of strong UV radiation, however, have opened possibilities for three-and four-photon iomzallon and auloiomzal1on experiments on Hz. A Wry recent rlirce~phoron iunrzarmn expenment [qJ has in fact underscored such possiblhties and their usefulness as spectroscoprc tuois It is Ulerefore of timely Interest 10 attempt rrla(ed thcorelwal sludles and I( may not even be LOO early to contemplate two-photon auIo1omzaCon Analogous expcrmIcn[s on muhlphoton 1onlzauon and autoromzatron ofalhalme cJrths [S,6] hJve shown .I vancty of surprlsmg feJrures. Thus, WC have been molwoted to undcrlakc a calculation of two-photon autoionlzatmn of H, m an BLtempt to explore the type of bcbavlor IlI$ mdy be expected in a molecule. In related theoretical work [7] we hdve found a number of new effects to be expected m multrphoton autoionlzation. effects due to the mlenslty necessary for the observation of the multrphoton process Itself. Our calculations should be relined m several aspects which wdl be discussed elsewhere. W11h the IntentIon of perhaps stimulatmg some experunentatlon along these Imcs, we present in this paper what we regard as somewhat prelimmary results which contdm, however, lhe essential features of the process. * Worh supported by J grJnr Iron1 Ihe Nar1onJ Science roundauon No.