The effect of low-energy neutrons on activation cross-section measurements was analyzed carefully and proved by the measured neutron spectra of T(d,n)4He and D(d,n)3He reactions. The 58Ni(n,p)58m+gCo and 64Zn(n,p)64Cu reactions were used to confirm this analysis, and their cross sections were measured accurately. In addition, their evaluated excitation functions are given.