We establish in this paper the existence of a long exact sequence in KKtheoryfor the füll free product of unital C*-algebras K-equivalent to nuclear ones. Wewill first prove the existence of e KK(S, D) such thaty^ (a) = ls in KK(S, S) and 7 * (a) = 1Din KK(D,D) for A1 and A2 K-nuclear and deduce the long exact sequences for thesealgebras. It was first conjectured by Cuntz in 1982 and only proved so far for C*-algebrashaving a one dimensional representation or for reduced (discrete) group C*-algebras. Wemake here a critical use of the reduced free product representation äs defined by Voiculescuäs well äs Skandalis' K-nuclearity notion.