Hydrogen adsorption on NiAl(110) has been investigated by means of helium atom scattering. In agreement with previous studies, hydrogen adsorption was found to be activated on this surface. Two ordered adsorbate structures could be identified after exposure of atomic hydrogen at 90 K: a c(2x2) and a (1x1)H saturation phase. The structures of the clean and hydrogen covered surfaces were determined from a quantitative analysis of the corresponding He-diffraction spectra. For the clean surface, a very shallow corrugation in which only the topmost Al atoms appear is obtained from He-diffraction data, whereas both Ni and Al atoms are visible in the corrugation determined with Ne diffraction. Surprisingly, the total corrugation amplitude determined for the c(2x2) structure was as shallow as the one of the clean surface. This very unusual fact may be taken as an evidence for the existence of delocalized hydrogen on this phase. The hydrogen adsorption site in the (1x1)H phase was determined to be the Ni-Ni bridge site, with a H-Ni bond length of 1.75 Angstrom, in agreement with previous ab initio calculations.