The 1h (one-hole) and 2h-1p (two-hole; one-particle) shake-up bands in the valence ionization spectrum of small carbon rings (C-4, C-6, C-8, C-10) are investigated up to 40 eV, using the one-particle Green＇s Function approach. Calculations have been performed using both the third-order algebraic diagrammatic construction [ADC(3)] scheme and the outer-valence Green＇s function (OVGF) approximation. The obtained ADC(3) results indicate a major fragmentation of lines into complex sets of 2h-1p satellites, even for outer-levels of Pi-character. The simulated ionization spectra provide striking structural signatures for the carbon rings vs. the carbon chains, that could be usefully exploited to discriminate these two types of clusters in plasma conditions. In general and in spite of the extent of the shake-up spreading, one can rather easily trace from our convolutions the energy degeneracies, and in the outer-valence region, the Sigma-Pi near-energy degeneracies which characterize the electronic structure of these doubly conjugated rings. In relationship to its doubly antiaromatic (i.e., polyynic) nature and lower symmetry, C-8 is subject to stronger many-body effects than the other rings. ADC(3) calculations on first-order saddle point forms of C-6 and C-10 indicate that thermal averaging of conformations could have a substantial effect on the spectral bands, in particular the shake-up ones. (C) 2000 American Institute of Physics. [S0021-9606(00)30510-4].