Quantum chemical calculations using density functional theory with the TPSS+D3(BJ) and M06-2X+D3(ABC) functionals have been carried out to understand the mechanisms of catalyst-free hydrogermylation/hydrostannylation reactions between the two-coordinate hydrido-tetrylenes :E(H)(L(+) ) (E=Ge or Sn, L(+) =N(Ar(+) )(SiiPr3 ); Ar(+) =C6 H2 {C(H)Ph2 }2 iPr-2,6,4) and a range of unactivated terminal (C2 H3 R, R=H, Ph, or tBu) and cyclic [(CH)2 (CH2 )2 (CH2 )n , n=1, 2, or 4] alkenes. The calculations suggest that the addition reactions of the germylenes and stannylenes to the cyclic and acyclic alkenes occur as one-step processes through formal [2+2] addition of the E-H fragment across the C-C π bond. The reactions have moderate barriers and are weakly exergonic. The steric bulk of the tetrylene amido groups has little influence on the activation barriers and on the reaction energies of the anti-Markovnikov pathway, but the Markovnikov addition is clearly disfavored by the size of the substituents. The addition of the tetrylenes to the cyclic alkenes is less exergonic than the addition to the terminal alkenes, which agrees with the experimentally observed reversibility of the former reactions. The hydrogermylation reactions have lower activation energies and are more exergonic than the stannylene addition. An energy decomposition analysis of the transition state for the hydrogermylation of cyclohexene shows that the reaction takes place with simultaneous formation of the Ge-C and (Ge)H-C' bonds. The dominant orbitals of the germylene are the σ-type lone pair MO of Ge, which serves as a donor orbital, and the vacant p(π) MO of Ge, which acts as acceptor orbital for the π* and π MOs of the olefin. Inspection of the transition states of some selected reactions suggests that the differences between the activation energies come from a delicate balance between the deformation energies of the interacting species and their interaction energies.