Density functional B3LYP and ab initio CASSCF calculations with the 6-31G* basis set have been performed to investigate various mechanisms of phenanthrene formation from biphenyl and naphthalene. Three competitive reaction pathways contributing to the PAH formation in combustion have been studied. The first one (RI) involves abstraction of a hydrogen atom followed by acetylene addition, ring closure, and hydrogen loss (disproportionation). In the other two routes, the acetylene addition is followed by H loss (disproportionation), H abstraction, ring closure, and H addition (R2) or by H addition and H abstraction (can be replaced by an H shift), ring closure, and H loss (disproportionation) (R3). Additionally, a new mechanism of phenanthrene formation from biphenyl is suggested. which does not require a presence of H radicals and involves [4+2] acetylene cycloaddition to biphenyl followed by H-2 elimination. Although the highest barrier for this reaction is calculated to be similar to45 kcal/mol. it can take place at high temperatures. The reaction steps of hydrogen elimination from radical intermediates can occur not only by direct hydrogen loss but also by H disproportionations, which typically have much lower barriers and are highly exothermic. Equilibrium constants and rate constants for various reaction steps have been computed using the transition state theory and ab initio energies and molecular structural parameters and can be used for future kinetic modeling of the PAH formation networks. The calculations demonstrate that the proposed hydrogen abstraction-acetylene addition (HACA) scheme provides viable mechanisms for the PAH formation and growth in flames.