In this paper we use a Choquet type theorem on adapted spaces to obtain or reobtain some results in harmonic analysis on semigroups. Thus we give a L ́evy]Khinchine formula for some negative definite functions defined on a com- mutative semigroup with neutral element, we prove that completely monotonic Žresp. alternating. functions are completely positive Žresp. negative. definite, we characterize the completely monotonic and the completely alternating func- tions defined on N* [ 1, 2, 3, . . . 4, and we consider a Stieltjes’ moment problem.