Helium atoms or hydrogen molecules are believed to be strongly bound within the interstitial channels (between three carbon nanotubes) within a bundle of many nanotubes. The effects on adsorption of a nonuniform distribution of tubes are evaluated. The energy of a single particle state is the sum of a discrete transverse energy E t (that depends on the radii of neighboring tubes) and a quasicontinuous energy E z of relatively free motion parallel to the axis of the tubes. At low temperature, the particles occupy the lowest energy states, the focus of this study. The transverse energy attains a global minimum value (E t = E min ) for radii near R min = 9.95Å for H 2 and 8.48A for 4 He. The density of states N (E) near the lowest energy is found to vary linearly above this threshold value, i.e. N (E) is proportional to (E − E min ). As a result, there occurs a Bose-Einstein condensation of the molecules into the channel with the lowest transverse energy. The transition is characterized approximately as that of a four dimensional gas, neglecting the interactions between the adsorbed particles. The phenomenon is observable, in principle, from a singular heat capacity.The existence of this transition depends on the sample having a relatively broad distribution of radii values that include some near R min .