Abstract: The glueing apparatus includes a pair of endless conveyor members (13, 15) whose active branches (13A, 15A) are parallel, with one superimposed above the other and spaced apart to an extent corresponding to the diameter of the rolls or logs (R) and moving in the same direction whereby to move the log forward. The upper active branch (15A) extends further than the lower active branch (13A). Unwind mechanism (31) for unwinding the tail (L) of the material of the log (R) is located upstream of the lower endless conveyor member (13) and controlled by an optical sensor which checks the length of said tail. Downstream of the lower endless conveyor member (13) a glue dispenser (58) dispenses glue from below onto the outer surface of the log. A subsequent rewinding station (R) is located downstream of the lower continuous conveyor member (13).