Phase transitions in centered-rectangular- and square-lattice-gas models have been studied by transfer-matrix methods, with the use of finite-size scaling ideas. The transition lines and critical exponents have been obtained for the p(2×1) and p(2×2) structures for the centered-rectangular model with several pairwise interactions and a three-body interaction. This model is of interest in that the p(2×1) and p(2×2) transitions belong to the universality class of the XY model with cubic anisotropy and hence the critical exponents are nonuniversal. As well, it is a simple model of O on W(110). The transition lines have also been obtained for a square-lattice-gas model with competing interactions, for the (2×1) and (2×2) ordered structures. The importance of finite-size effects is demonstrated for both models.