The chemistry of naphthalene radical cation and its derivatives (C10Hn+, n = 6,7,8,9) has been studied with molecules and atoms of interstellar interest in a selected ion flow tube. The radical cation C10H8+ is unreactive with H-2, CO, H2O, and NH3 but reacts with H, O, and N atoms. Adduct formation is the only channel detected in the case of reaction with H atoms, but additional channels contribute in reactions between C10H8+ and O and N atoms; these latter reactions proceed through novel reaction pathways via C and CH abstraction, leading to the formation of the stable compounds CO and HCN, respectively. The closed-shell naphthylium cation C10H7+ is essentially unreactive with atoms but associates via nucleophilic addition with most of the molecules studied. The reaction kinetics are close to saturation in the accessible helium pressure range. The naphthyne radical cation C10H6+ does not react with H-2, CO, or H2O but forms an adduct with NH3 at a moderate rate. Reactions with atoms were found to be very similar to those of C10H8+ The implications of these results for the stability of polycyclic aromatic hydrocarbon cations in the interstellar medium are briefly discussed.