Excitation functions of the reactions 185Re[(α,n); (α,2n); (α,3n)] and 187Re[(α,n); (α,2n); (α,3n); (α,4n)] were investigated up to 50 MeV using the stacked-foil activation technique and high-purity germanium γ-ray spectroscopy method. Since the natural rhenium used as a target has two odd-mass stable isotopes of abundance 37.4% (185Re) and 62.6% (187Re), their activation in some cases gives the same residual nucleus through different reaction channels, but with very different Q values. In such cases, the individual reaction cross sections are separated with the help of the ratio of theoretical cross sections. The experimental cross sections were compared with the theoretical predictions considering equilibrium as well as pre-equilibrium contributions using code ALICE/90. It was found that the initial exciton configuration n0 = 4 (4p0h) appears to give a good fit to the experimental data. To the best of our knowledge, the excitation functions for 185Re[(α,n); (α,2n); (α,3n)] and 187Re[(α,3n); (α,4n)] reactions were measured for the first time. PACS No.: 25.55.e