A painstaking comparison of laboratory gas-phase spectra of the naphthalene cation with an extensive set of astrophysical spectra was carried out. In the vicinity of both naphthalene features, found in the laboratory experiment, we detected relevant interstellar features. The strongest of them is situated at 6710.5 Angstrom, which is reasonably close to the laboratory feature at 6706.5 Angstrom and which is also of comparable width, i.e. about 20 Angstrom. The second feature was found at 6493 Angstrom - also close to the 6488.4-Angstrom laboratory band of a similar width. The structures can be observed only in spectra of O stars because of the growing stellar line contamination in colder objects. The possible third feature is intertwined with a strong stellar helium line, but the unusual strength of the latter suggests that this naphthalene cation band is present as well as the two former ones. We estimated the column density of the carrier, for the reddening value E(B - V) = 1.0, as roughly 4 x 10(15) cm(-2). The lack of precise wavelength coincidence between laboratory and observed features, however, makes the identification uncertain and further laboratory and observational works are both highly desirable.