The efforts to reduce NOx pollutants have stimulated a large interest in the understanding of the elementary processes for NO transformation on transition metal surfaces. Periodic density-functional calculations have been performed for the molecular and dissociative chemisorption of NO on Pd and Rh(100) and (111) surfaces, with generalized gradient approximation exchange-correlation functionals. The periodic systems are modeled by two-dimensional palladium or rhodium slabs with frozen geometry, on which a NO, N, O, or (N+O) adlayer is set. On Pd and Rh(100) at a coverage of 0.5 monolayer (ML), the bridge site is the most stable one with respective binding energies of -1.54 and -2.18 eV. On the (111) surfaces, at a coverage of 0.33 ML, the threefold hollow sites are favored with binding energies of -2.0eV for Pd(111) and -2.18 eV for Rh(111). For the dissociated structures, the mixed coadsorption of N and O is favored in most cases compared to separated domains. The chemisorption of NO, N, or O is stronger on Ph surfaces than on Pd ones but the stability gain is larger for the atomic chemisorption. The absolute values of binding energies decrease with the coverage. The NO dissociation is exothermic only for Rh at low coverage, while it is endothermic on Pd due to smaller atomic binding energies. This reaction becomes more endothermic when the coverage increases.