We study harmonic analysis on cocommutative KPC-hyper-groups, which is a generalization of DJS-hypergroups, introduced by Kalyuzhnyi, Podkolzin and Chapovsky. We prove that there is a relationship between the associated measures $mu$ and $gamma mu$, where $mu$ is a Radon measure on KPC-hypergroup $Q$ and $gamma$ is a character on $Q$.
