Noname manuscript No. (will be inserted by the editor) Some asymptotic limits of reaction–diffusion systems appearing in reversible chemistry Fiammetta Conforto · Laurent Desvillettes · Roberto Monaco Received: date / Accepted: date Abstract This paper concerns reaction–diffusion systems consisting of three or four equations, which come out of reversible chemistry. We introduce differ- ent scalings for those systems, which make sense in various situations (species with very different concentrations or very different diffusion rates, chemical reactions with very different rates, etc.). We show how recently introduced mathematical tools allow to prove that the formal asymptotics associated to those scalings indeed hold at the rigorous level. Keywords Reaction-Diffusion equations · Reversible chemistry · Singular Perturbations 1 Introduction A generic reversible reaction like µ 1 A 1 + ... + µ p A p ⇋ ν 1 A 1 + ... + ν p A p (1) This work has been supported by the French “ANR blanche” project Kibord: ANR-13- BS01-0004, by Universit´ e Sorbonne Paris Cit´ e, in the framework of the “Investissements d’Avenir”, convention ANR-11-IDEX-0005, and by the National Group of Mathematical Physics (INdAM–GNFM). F. Conforto Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Universit` a di Messina, V.le Stagno d’Alcontres 31, 98166 Messina, Italy E-mail: fiammetta.conforto@unime.it L. Desvillettes Univ. Paris Diderot, Sorbonne Paris Cit´ e, Institut de Math´ ematiques de Jussieu - Paris Rive Gauche, UMR 7586, CNRS, Sorbonne Universit´ es, UPMC Univ. Paris 06, F-75013, Paris, France E-mail: desvillettes@math.univ-paris-diderot.fr R. Monaco DIST, Politecnico di Torino, Viale Mattioli 39, 10125 Torino, Italy E-mail: roberto.monaco@polito.it