Previous uv photoemission (UPS) measurements have shown that extramolecular relaxation-polarization shifts (ERPS) of the valence molecular orbitals of absorbed organic molecules (i.e., shifts in orbital binding energies from free-molecule values) are essentially the same for all adsorbate orbitals of a given molecule-surface system (except for those high-lying orbitals directly involved in forming the chemisorption bond to the surface). There now exists much experimental evidence, compiled in this paper, for this pattern of essentially uniform ERPS. Although not understood on theoretical grounds, the observed uniformity of ERPS is very important, and perhaps crucial, to the use of UPS in surface chemistry. Also, we report here the first significant deviations from the pattern of uniform ERPS, which occur for a few deeper-lying valence orbitals of several organic molecules. These anomalies can be understood on the basis of the atomic-orbital character of the molecular orbitals, as determined by a straightforward molecular-orbital calculation. Furthermore, it appears that such calculations make it possible to predict which orbitals of which molecules might exhibit anomalous ERPS. Thus these anomalies do not represent a serious impediment to UPS studies of surface chemistry via the uniform-ERPS assumption. Finally, the interpretation of an anomaly for chemisorbed formaldehyde (H2CO) appears to resolve a long-standing controversy between theory and experiment regarding the ordering of orbitals in the free molecule. © 1976 The American Physical Society.