The invention relates to an aeroengine after-body assembly comprising an exhaust casing made of metal having a plurality of arms extending radially between an inner shroud and an outer shroud. The assembly comprises at least one axisymmetric part made of composite material extending between an upstream end fastened to said exhaust casing and a downstream end that is free. In accordance with the invention, the axisymmetric part has an annular portion at its upstream end, which annular portion includes a plurality of slots defining between them a plurality of resilient fastener tabs. Each slot co-operates with an arm of the exhaust casing, which further includes fastener parts attached to the resilient fastening tabs.