Allylation reactions of CH2O by germanium and tin complexes, AF4(CH2CH=CH2)- (A = Ge, Sn), are studied by ab-initio MO calculations and compared with the similar reactions of silicon complex, SiF4(CH2CH=CH2)- reported previously. We determine fully optimized geometries of the tetra-, penta-, and hexacoordinate compounds, AF3+n(CH2CH--CH2)n- and AF4(OCH2)-(CH2CH=CH2)- (A = Ge, Sn; n = 0, 1), along the reaction path. Pentacoordinate AF4(CH2CH=CH2)- complexes have enhanced nucleophilicity at the allylic gamma-carbon and significant Lewis acidity to form hexacoordinate complexes by the addition of CH2O. These hexacoordinate complexes AF4(OCH2)(CH2CH=CH2)- are predicted to exist as stable intermediates before the transition state, so that they may be detected experimentally. The structures of the hexacoordinate transition state in the allylation reactions are also determined, assuming that the cyclic chair form is preferable to the linear form, as reported in the previous investigation on the Si compounds. The reactivity of the Ge and Sn complexes is expected to be greater than that of the Si compound because of the lowering of the potential energy barriers. When CH(CH3)O reacts with AF4(CH2CH-CH2)-, the energy differences between the axial and equatorial forms of the transition state are 2 and 5 kcal/mol for Ge and Sn, respectively, in comparison with 13.6 kcal/mol for the Si compounds, so that the stereoselective control, which is observed in the Si complexes, may be diminished in the Ge and Sn complexes.