The 36Cl(n,p)36S and 36Cl(n,alpha)33P reaction cross sections have been studied with resonance neutrons at the linear accelerator GELINA of the IRMM in Geel (Belgium) and have been determined up to approximately 250 keV using the time-of-flight technique. In this energy region, 17 resonances were observed, whereas eight were identified before. For some resonances the resonance strength, the spin, and the total width could be determined. From the obtained cross section data, the MACS has been calculated by numerical integration. These updated MACS values were used in stellar models to trace the origin of the rare isotope 36S.