We have made a statistical mechanical study of a vicinal surface with adsorption with coverage Theta being less than 1. In the case of Langmuir adsorption, where the lateral interactions among the adsorbates are absent, the universal behavior of a vicinal surface-Gruber-Mullins-Pokrovsky-Talapov (GMPT) behavior persists although the step tension, the step stiffness and the roughening transition temperature are modified by adsorbates. The effect of lateral attraction among adsorbates is the emergence of the inter-step attraction mediated by the density fluctuation of the adsorbate., which causes non-GMPT behavior such as first-order transition in equilibrium crystal shape and thermal step bunching. (C) 2002 Elsevier Science B.V. All rights reserved.