The characteristics of the interaction between the pi cloud of naphthalene and up to two H2O or H2S molecules were studied. Calculations show that clusters formed by naphthalene and one H2O or H2S molecule have similar geometric features, and also present similar interaction energies. Our best estimates for the interaction energy amount to -2.95 and -2.92 kcal/mol for H2O and H2S, respectively, as obtained with the CCSD(T) method. Calculations at the MP2 level employing large basis sets should be avoided because they produce highly overestimated interaction energies, especially for hydrogen sulfide complexes. The MPWB1K functional, however, provides values pretty similar to those obtained with the CCSD(T) method. Although the magnitude of the interaction is similar with both H2X molecules, its nature is somewhat different: the H2O complex presents electrostatic and dispersion contributions of similar magnitude, whereas for H2S the interaction is dominated by dispersion. In clusters containing two H2X molecules several minima were characterized. In water clusters, the total interaction energy is dominated by the presence of a O-H...O hydrogen bond and, as a consequence, structures where this contact is present are the most stable. However, clusters containing H2S show structures with no interaction between H2S moieties which are as stable as the hydrogen bonded ones, because they allow an optimal H2S...naphthalene interaction, which is stronger than the S-H...S contact. Therefore it is possible that in larger polycycles hydrogen sulfide molecules will be spread onto the surface maximizing S-H...pi interactions rather than aggregated, forming H2S clusters.