(EN) Floor sill system (9) for a displaceable sash as a sliding sash (3) or displaceable lift-and-slide sash of a window or of a door (1), comprising a receiving groove (10) in a floor sill profile (11) for receiving a guide web (12) for a running rail (15) which has the running rollers (13) of sash-side running carriages (14) and which is arranged opposite the sliding sash (3) on the upper side of the floor sill profile (11), wherein the guide web (12) can be engaged over its entire length into the receiving groove (10) with a form or force fit. There is preferably provided at least one adapter profile (16) which, by way of a connecting means (18) equipped convexly on its underside (17), can engage into the receiving groove (10) in the floor sill profile (11) with a form and/or force fit, and has on its upper side (19) a receiving groove (20) which is formed congruently to the receiving groove (10) in the floor sill profile (11), wherein the receiving groove (20) of the adapter profile (16) receives the guide web (12) on its upper side and, together with the upper side (19), forms a surface-flush, barrier-free contact. Furthermore, a visible bearing surface (21, 22) is formed on the respective sides of the adapter profile (16) and against which there can be laid, to the inner side (23) of the room, an inner floor surface (24) and, to the outer side (25) of the room, selectively different expansion profiles (26, 27) for transition to the outer floor surface (28), preferably for barrier-free transitions.