We investigate the cyclic polyenes (annulenes) CMHM, described by the Pariser-Parr-Pople (PPP) model, by means of the approximate coupled-pair theories (ACP, ACPQ). For the systems with the spectroscopic value of the PPP resonance integral beta = 2.5 eV, the ACP method breaks down for M greater than or equal to 446 and the ACPQ method - for M greater than or equal to 198. In the ACPQ method, for M greater than or equal to 174, two close lying solutions have been observed that become quasi-degenerate for M greater than or equal to 198. The results indicate that the ACP and ACPQ methods cannot be applied to the one-dimensional metallic case. (C) 2002 Elsevier Science B.V. All rights reserved.