In this paper, we characterize, for 1≤$p$<∞, the multiple ($p$, 1)-summing multilinear operators on the product of$C(K)$spaces in terms of their representing polymeasures. As consequences, we obtain a new characterization of ($p$, 1)-summing linear operators on$C(K)$in terms of their representing measures and a new multilinear characterization of$L$_{∞}spaces. We also solve a problem stated by M.S. Ramanujan and E. Schock, improve a result of H. P. Rosenthal and S. J. Szarek, and give new results about polymeasures.