The ability of cyclopentadienyl type derivatives of corannulene C2oH~, 3 and fullerene lh-C6o to form vl-%Tt-complexes and the problem of their existence is discussed. MNDO/PM3 calculations of half-sandwich complexes @-~-MC20HIs, rls-r~-MC20Hl5 *, @-r~-MC60Hs, rls-,'t-MC60Hs § and sandwich complexes 2riS-,~-M(C20Hjs)2, 2rI-~-n-M(C20HIs)2, 2rls-rt-M(C60Hs)2 (M = Si, Ge, Sn, Pb) were performed. For all systems studied, local minima were found on corresponding potential energy surfaces and the heats of formation, geometric parameters, and distributions of effective atomic charges were calculated. Sandwich complexes are most likely to exist with M = Si and Ge. The energy and geometric characteristics of rlS-rc-complexes of corannulene were compared with those of rlS-n-complexes of fulterene lh-C60, It was concluded that the results of quantum-chemical calculations of sandwich type corannulene derivatives can be used for simulation of the geometry and electronic structure of analogous complexes of fullerene lh-C60.