Density functional theory is employed to study Pd and Pd/Ni alloy monatomic chain-functionalized metallic single walled carbon nanotubes(SWNT(6,6)) and semiconducting SWNT(10,0), and their interactions with hydrogen molecules. The stable geometries and binding energies have been determined for both isolated chains and chains on SWNT surfaces. We found that continuous Pd and Pd/Ni chains form on SWNTs with geometries close to stable geometries in the isolated chains. Ni alloying improves stability of the chains owing to a higher binding energy to both Pd and C atoms. The physical properties of SWNTs are significantly modified by chain functionalization. SWNT(10,0) is transformed to metal by either Pd or alloy chains, or to a smaller band gap semiconductor, depending on the Pd binding site. From calculations for H-2 interactions with the optimized chain-SWNT systems, the adsorption energy per H atom is found to be about 2.6 times larger for Pd/Ni chain-functionalized SWNTs than for pure Pd chain-functionalized SWNTs. Band structure calculations show that the SWNT(10,0) reverts back to semiconductor and SWNT(6,6) has reduced density of states at the Fermi level upon H-2 adsorption. This result is consistent with the experimentally observed increase of electrical resistance when Pd-coated SWNTs are used as H-2 sensing materials. Finally, our results suggest that Pd/Ni-SWNT materials are potentially good H-2-sensing materials.