Un langage algébrique particulier

— 11 is well-known that thefamily of context-free languages is a full principal AFL. It thus contains a largestfûll sub-AFL, denoted Nge, consisting ofthe languages which are notfull generators. One ofthe major problems (still unsolved) is to know whether this AFL is principal or not. The main resuit in this direction states that Ngestrictly contains thefamily Gre ofthe Greibach languages ( — the substitution closure ofthe linear and one counter languages'family). To get a better understanding of hovo Nge is built, one possible way is to try tofînd what makes this inclusion strict; that is tofînd subfamilies on which Nge and Gre do coïncide. It was conjectured [8] that thefamily ofIRS languages was such a sub-family. We disprove this conjecture, getting thus a new kind of languages that lie between Nge and Gre. Surprisingly, our counter example gives also négative answers to two different questions, thefîrst about the notion of adhérence [9], the second dealing with rational indexes [11].