  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.}
