Abstract: The invention relates to the sealing of the cavity from which air is bled off to the cabin, which cavity is delimited, on the one hand, by the external shell of the compressor and an annular structure connected to the shell, and, on the other hand, by the external casing of the diffuser grating and a strut connected to said external casing and to an external engine casing shell fastened to the annular structure. A first seal is fitted in a first groove provided around the upstream part of the external casing of the diffuser grating, the strips of this first seal bearing on the downstream end of a first projection integral with the annular structure. A second seal is fitted in a second groove provided under said annular structure, the strips of this second seal bearing on the downstream end of a second projection integral with said annular structure and on the end of a third projection formed on the upstream part of the external casing of the diffuser.