Proton and a-particle spectra have been measured at backward angles in the ¹²C + ⁹³Nb reaction at E(¹²C)=37.5-60 MeV and in the ¹⁶O+⁹³Nb reaction at E(16O)=54-75 MeV. The inclusive particle spectra generally are in good agreement with the statistical model calculations except for the a spectra in the ¹²C-induced reaction at beam energies of 37.5-42.5 MeV which are close to the Coulomb barrier in the entrance channel. In these cases the evaporation peak is up to 2 MeV lower than its expected position from the statistical model predictions. Gamma-multiplicity-gated a spectra, measured in the same reaction, also show the aforementioned discrepancy. These observations reveal that the conventional statistical model cannot explain the a-particle spectra in the ¹²C-induced reactions near the Coulomb barrier.