A cutter bit assembly is composed of a carrier or holder secured or integral with a coal plough and a cutter part detachably secured to the holder. The holder has a head piece with opposite plane faces extending transversally to the cutting direction. A bore in the head piece opens to these faces and extends parallel to the cutting direction. The cutter part has a plane face engageable on one of the transverse faces of the head piece and a projection and recess on these engageable faces prevents rotation of the cutter part. A threaded member either integral with or separate from the cutter part extends through the bore in the head piece and receives a nut bearing on the other of the transverse faces and used to detachably secure the cutter part to the head piece.