The rewinding machine (1) comprises: a winding station (3) with winding members (5, 7) operated by winding motors (8.1, 8.2); an unwinder (31.1, 31.2) with an unwinding member (35.1, 35.2) operated by at least one unwinding motor (38.1, 38.2); guide roller (43.1, 43.2) along a feed path (P) of the web material (N, N2). There is associated with the guide roller (43.1, 43.2) at least one load sensor (42.1, 42.2), adapted to detect a parameter proportional to the tension of the web material (N; N2) guided around the guide roller (43.1, 43.2). There is also provided a control unit (71) adapted to modulate a difference in speed between the winding members (5, 7) and the unwinding member (35.1, 35.2) as a function of a signal coming from the load sensor (42.1, 42.2).