The 18O(p,α)15N and 17O(p,α) 14N reactions are of primary importance in several as-trophysical scenarios, including nucleosynthesis inside Asymptotic Giant Branch stars and oxygen and nitrogen isotopic ratios in meteorite grains. They are also key reactions to understand exotic systems such as R-Coronae Borealis stars and novae. Thus, the measurement of their cross sections in the low energy region can be crucial to reduce the nuclear uncertainty on theoretical predictions, because the resonance parameters are poorly determined. The Trojan Horse Method, in its newly developed form particularly suited to investigate low-energy resonances, has been applied to the 2H(18O, α15N)n and 2H(17O,α14N)n reactions to deduce the 18O(p,α)15N and 17O(p,α)14N cross sections at low energies. Resonances in the 18O(p,α)15N and 17O(p,α)14N excitation functions have been studied and the resonance parameters deduced.