A process for weaving superimposed ribbons which are stitched to each other, comprising a sequence of successive cycles, each cycle comprising the steps of: - providing on a loom a first plurality of warp threads which are intended for weaving a lower ribbon, extended transversally between a first side thereof and a second side thereof, subdividing said first plurality of warp threads between a first upper row of threads and a first lower row of threads so as to define between the first rows of threads a first shed, - providing on the loom a second plurality of warp threads which are intended for weaving an upper ribbon, extended transversally between a first side thereof and a second side thereof, subdividing said second plurality of warp threads between a second upper row of threads and a second lower row of threads so as to define between the second rows of threads a second shed, the second lower row of threads being positioned higher than the first upper row of threads, characterised by - passing a first weft thread with a first arm which is able to be pivoted transversely to the advance direction through the first shed between said first side and said second side of the lower ribbon where it is engaged by a first hook located at said second side of said lower ribbon, - passing a second weft thread with a second arm which is able to be pivoted transversely to the advance direction through the second shed between said first side and said second side of the upper ribbon where it is engaged by a second hook located at said second side of said upper ribbon, - compacting the first weft thread and the second weft thread against the respective preceding weft threads, - moving at least one or more of the warp threads of the lower ribbon between the first upper row and the first lower row so as to bind the first weft thread, - moving at least one or more of the warp threads of the upper ribbon between the second upper row and the second lower row, so as to bind the second weft thread, - providing on the loom at least one stitching thread which extends between the pluralities of warp threads (21, 31), the at least one stitching thread being moved, at the time of one or more of the cycles, between the second upper row and the first lower row, and vice versa, so as to bind together the first and second weft thread (23, 33). - providing on a loom a first plurality of warp threads which are intended for weaving a lower ribbon, extended transversally between a first side thereof and a second side thereof, subdividing said first plurality of warp threads between a first upper row of threads and a first lower row of threads so as to define between the first rows of threads a first shed, - providing on the loom a second plurality of warp threads which are intended for weaving an upper ribbon, extended transversally between a first side thereof and a second side thereof, subdividing said second plurality of warp threads between a second upper row of threads and a second lower row of threads so as to define between the second rows of threads a second shed, the second lower row of threads being positioned higher than the first upper row of threads, characterised by - passing a first weft thread with a first arm which is able to be pivoted transversely to the advance direction through the first shed between said first side and said second side of the lower ribbon where it is engaged by a first hook located at said second side of said lower ribbon, - passing a second weft thread with a second arm which is able to be pivoted transversely to the advance direction through the second shed between said first side and said second side of the upper ribbon where it is engaged by a second hook located at said second side of said upper ribbon, - compacting the first weft thread and the second weft thread against the respective preceding weft threads, - moving at least one or more of the warp threads of the lower ribbon between the first upper row and the first lower row so as to bind the first weft thread, - moving at least one or more of the warp threads of the upper ribbon between the second upper row and the second lower row, so as to bind the second weft thread, - providing on the loom at least one stitching thread which extends between the pluralities of warp threads (21, 31), the at least one stitching thread being moved, at the time of one or more of the cycles, between the second upper row and the first lower row, and vice versa, so as to bind together the first and second weft thread (23, 33).