Critical properties of the two-dimensional order-disorder phase transitions of the p(2×2) and the (3 × 3) R30°superstructures of sulfur chemisorbed on Ru(001) were determined by spot-profile analysis using high-resolution low-energy electron diffraction. Both transitions are continuous, as evident from the power-law behavior observed for 0.01≤t≤0.1 (t=T/Tc-1) and from the values obtained for the critical exponents. For smaller t the phase transitions are finite-size rounded by an interaction of the superstructure domains with steps (average distance between steps ∼275). The values of the effective exponents β of the order parameter, ν of the correlation length, γ of the susceptibility, and the exponent η [only determined for p(2×2)] fall close to the values theoretically predicted for the four-state and three-state Potts universality classes, respectively. Deviations of experimental values from Potts values, found for β and γ, are attributed to corrections to scaling which in part might be specific of the lattice gas. Additional experiments on vicinal surfaces with higher step densities show that pinning of the superstructure domains at monoatomic steps limits the correlation length to values below the average terrace width. The finite-size-induced effects are quantitatively compatible with predictions from finite-size scaling theory. © 1994 The American Physical Society.