Comparaisons des exposants \`a l'int\'erieur d'un paquet d'Arthur archim\'edien

Generalizing the proof – by Hecht and Schmid – of Osborne’s conjecture we prove an Archimedean (and weaker) version of a theorem of Colette Moeglin. The result we obtain is a precise Archimedean version of the general principle – stated by the second author – according to which {\it a local Arthur packet contains the corresponding local $L$-packet and representations which are more tempered.}