Minimal Realizations and State

State space transformations in the max-algebraic system theory for Discrete Event Systems (DES) are discussed. Some transformations between diierent realiza-tions of a given impulse response of a DES are suggested and their limitations are illustrated. It is explained why a general result seems hard to prove. R esum e: Nous discutons certaines transformations d' etat dans la th eorie des syst emes pour une classe de syst emes a ev enements discrets (SED). On propose des transformations entre dii erentes r ealisations de la r eponse impulsionelle d'un SED max-alg ebrique donn e. Nous illustrons les limitations de ces transformations et nous expliquons pourquoi un resultat g en eral sera diicile a prouver.