Series which are both max-plus and min-plus rational are unambiguous Sylvain Lombardy and Jean Mairesse This paper shows that two families of formal power series over a free monoid, the unambiguous series on the on hand, and the max-+ and min-+ rational series on the other hand, are actually the same family. The two classes of rational series have nice properties (decidability of equivalence or sequentiality) and therefore this unify several previous results. We give an efficient procedure to build an unambiguous automaton from a max-plus automaton and a min-plus one that recognize the same series. The proof of this result uses several decision results; most of them have been previously proved in particular cases (integer or positive values), we give here effective proofs and extend them to the (R,max,+) semiring.