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We study orbital integrals and invariant eigendistributions for the symmetricpair (g,h)=(gl(4,R),gl(2,R)*gl(2,R)). Let q=g/h and let N be the set ofnilpotents of q. We first obtain an asymptotic behavior of orbital integralsaround nonzero semisimple elements of q. We study eigendistributions aroundsuch elements and give an explicit basis of eigendistributions on q-N given bya locally integrable function on q-N.

Distributions propres invariantes sur la paire sym\' etrique (gl(4,R),gl(2,R)*gl(2,R))