We present results of Ar adsorption isotherms at very low coverages in the first layer and, beyond monolayer completion, on bundles of close-ended single-walled carbon nanotubes. The low coverage results were used to determine the isosteric heat of adsorption and the binding energy of Ar in the groove sites in the first layer. The higher coverage results show evidence of the possible formation of a second-layer groove phase, beyond monolayer completion. Our results for higher coverages are compared with recent computer simulations for this system.