The reactions 10 B(p,α) 7 Be and 11 B(p,α) 8 Be are studied at thermonuclear energies using DWBA calculations. For both reactions, transitions to the ground states and first excited states are investigated. In the case of 10 B(p,α) 7 Be, a resonance at E Res = 10 keV can be consistently described in the potential model, thereby allowing the extension of the astrophysical S-factor data to very low energies. Strong interference with a resonance at about E Res = 550 keV require a Breit-Wigner description of that resonance and the introduction of an interference term for the reaction 10 B(p,α 1 ) 7 Be * . Two isospin T = 1 resonances (at E Res1 = 149 keV and E Res2 = 619 keV) observed in the 11 B+p reactions necessitate Breit-Wigner resonance and interference terms to fit the data of the 11 B(p,α) 8 Be reaction. S-factors and thermonuclear reaction rates are given for each reaction. The present calculation is the first consistent parametrization for the transition to the ground states and first excited states * current address 1 at low energies.