The weaving machine with a weft monitoring insertion system (1) for a large number of different weft threads (11, 11', 11") comprises a weft insertion member (6, 60), thread brakes (3), a weft thread selector (4) for the serving of a thread (11, 11', 11") or of more than one thread at the same time, a thread monitor (51) for weft threads (11) which are correctly inserted, and an electronic and programmable control member (8) for the setting of the thread brakes. The weft threads (11), when correctly inserted, form incoming angles (.alpha.) at the thread monitor in the presence of a deflection which depend on the choice of the weft thread. Utilizing the thread monitor (51) a signal can be produced for the control member (8) which is dependent on the incoming angle and the thread tension. Control signals can be calculated and produced in the control member as a result of this signal and as a result of information on the current serving of the weft thread or of the weft threads, i.e. of the presentation of the threads to be inserted through the weft thread selector (4).