Low-energy electron diffraction (LEED) measurements were made for N-2 and CO adsorption on Ag(lll) at temperatures (T) >25 K. The results indicate that at coverages up to a saturated monolayer, N-2 and CO each forms a rotated incommensurate hexagonal structure. The first layer of CO is somewhat more strongly bound to the surface than that of N-2, and has a monolayer lattice spacing that is similar to 5% smaller. This result is interpreted as being due to a more perpendicular orientation of the CO molecules. The isobaric expansion coefficient for the CO monolayer is considerably smaller than that of N-2, which may also be related to a more perpendicular orientation of CO molecules. The epitaxial rotation angle measured for N-2 is close to the Novaco-McTague prediction for the lowest temperatures measured; the angle for CO, on the other hand, is very different from the predictions. No additional order was noted upon adsorption of the N-2 second layer. Adsorption of a CO second layer, however, produces an oblique and mutually commensurate bilayer structure.