We study the structure of the hydrogen atom when placed in a high-frequency, superintense laser field, within the framework of a nonperturbative theory recently developed for this purpose. The theory predicts that in the high-frequency limit the atom is stable against decay by multiphoton ionization, and that its structure is determined by a time-independent Schrödinger equation containing a dressed Coulomb potential. The laser frequency and the intensity I enter only combined in the parameter 0=I1/2-2 a.u. We first analyze the symmetry of the eigenvalue problem for the case of linear polarization under consideration and adopt an appropriate classification scheme for the levels. The small-0 limit of the levels is obtained analytically. In the large-0 limit scaling laws are derived for the 0 dependence of the eigenvalues and eigenfunctions. At finite 0 we have carried out a very accurate numerical computation over an extended range of 0 values (00 200 a.u.) for a number of symmetry manifolds, by diagonalization of the Hamiltonian in a Gaussian basis. The correlation diagrams relating the small- and large-0 limits exhibit several avoided crossings. The binding energies show an overall decrease with 0, in some cases preceded by an increase through a maximum. For the ground state this decrease is quite steep. The extreme distortion of the atomic structure accompanying it is studied. It is shown that, with increasing 0, the (oscillating) electronic cloud undergoes radiative stretching, which eventually culminates at large 0 in its splitting into two parts (dichotomy). The consequences of our findings for the experimental energy spectrum of the ejected electrons are considered. © 1990 The American Physical Society.