A periodic n-dependence has been found in the lowest excitation energies of the tube-like fullerenes C60+10n (n = 1, 2,...), each consisting of a pair of the bisected caps Of C-60 and a single-wall cylinder. By inspection of the periodicity, the tube-like fullerenes are classified into three series of C70+30, C80+30 and C90+30m (m = 0,1,2....). The analysis with the Pauling bond order indicates the formation of a pseudo pi-conjugation on each layer of the cyclopentaphenylene structure with 30 C-atoms in the central cylindrical parts of the tube-like fullerenes. (C) 2003 Elsevier Science B.V. All rights reserved.