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We establish the invariant trace formula (\`a la Arthur) for the ad\'eliccovers of connected reductive groups over a number field, under the hypothesisthat the trace Paley-Wiener theorem is verified for all Levi subgroups at thereal archimedean places. For instance, this hypothesis can be verified for themetaplectic covers of GL(n), or the twofold metaplectic cover of Sp(2n). Wealso give simple trace formulae when the test function satisfies certaincuspidality properties.

La formule des traces pour les rev\^etements de groupes r\'eductifs connexes. IV. Distributions invariantes