Abstract: Let K be a subset of k positive integers. By a K-intersecting family F, we mean a family of subsets of S={1,2,...,n} such that for any A,B in the family F,|A(intersect)B| is an element of K. The purpose of the talk is to present a result due to Snevily: for such a family F, |F|< = the sum of the binomial coeffs (n-1)Ci,i ranging from 0 to k. This generalizes an earlier proved result for the set K={1,2,...k}.