Let A= { A1, … , Ap} and B= { B1, … , Bq} be two families of subsets of [n] such that for every i∈ [p] and j∈ [q] , |Ai∩Bj|=cd|Bj|, where cd∈[0,1] is an irreducible fraction. We call such families cd-cross intersecting families. In this paper, we find a tight upper bound for the product | A| | B| and characterize the cases when this bound is achieved for cd=12. Also, we find a tight upper bound on | A| | B| when B is k-uniform and characterize, for all cd, the cases when this bound is achieved. © 2020, Springer Japan KK, part of Springer Nature.