Title of Paper :Mislin genus of maps Author(s) : Jianzhong Pan and Moo Ha Woo AMS Classification numbers :55D99 Addresses of Authors: Jianzhong Pan Institute of Math.,Academia Sinica ,Beijing 100080 ,China email:pjz@math03.math.ac.cn and Moo Ha Woo Department of Mathematics Education , Korea University , Seoul , Korea Text of Abstract (try for 20 lines or less): In this paper, we prove that the Mislin genus of a (co-)H-map between (co-)H-spaces under certain natural conditions is a finite abelian group which generalizes results in Zabrodsky, McGibbon and Hurvitz