The thermodynamics of adsorption of light alkanes and alkenes (${\text{CH}}_4$, ${\text{C}}_2{\text{H}}_6$, ${\text{C}}_2{\text{H}}_4$, ${\text{C}}_3{\text{H}}_8$, and ${\text{C}}_3{\text{H}}_6$) in single-walled carbon nanotube bundles is studied by configurational-bias grand canonical Monte Carlo simulation. The bundles consist of uniform nanotubes with diameters in the range $11.0\text{Å}\le D\le 18.1\text{Å}$, arranged in the usual close-packed hexagonal lattice. The phase space is systematically analyzed with calculations for adsorption at room temperature and reduced pressure range of $8.7\times {10}^{-9}<p/p_0<0.9$. The simulation results are interpreted in terms of the molecular nature of the adsorbate and the corresponding solid-fluid interactions. It is shown that confinement in the internal volume of the bundle (interstitial and intratubular) is energetically more favorable than physisorption on the external surface (grooves and exposed surfaces of peripheral tubes), as indicated by the curves of isosteric heat as a function of reduced pressure. However, the zero-loading properties suggest a crossover point to this behavior for $D\sim 18–19\text{Å}$. When interstitial confinement is not inhibited by geometrical considerations, it is possible to establish the following ordering of the zero-loading isosteric heat by type of adsorption site: ${\left(q_{\text{st}}^0\right)}^{\text{interstitial}}>{\left(q_{\text{st}}^0\right)}^{\text{intratubular}}>{\left(q_{\text{st}}^0\right)}^{\text{grooves}}>{\left(q_{\text{st}}^0\right)}^{\text{surface}}$.