Types et suites symetriques dansL p , 1≦p<+∞,p≠2

We prove that every normalized sequence inL ^p , weakly null ifp>2 and equivalent to the unit vector basis ofl ² if 1≦p<2, has for allε>0 a subsequence which is 2(1+ε)-symmetric. This result was known forp=1 (H.P. Rosenthal) andp∈N (W.B. Johnson, B. Maurey, G. Shechtman, L. Tzafriri). Here, we use the techniques of stability which were introduced by J.L. Krivine and B. Maurey: as well as providing new results, this approach unifies and simplifies previous known results.