SYSTEM ATTACHING, SECURING AND RELATIVELY ROTATING A TOILET SEAT AND COVER formed by two rotating components, cover and seat, and by one or more shaft-pieces (13, 14, 15, 16, 17, 18) that is or are fitted in the housings (21, 23) of the toilet cover and seat, or its extensions, to allow rotation between said rotating components, cover and seat, wherein the system contains: - at least one moveable shaft-piece, where this moveable shaft-piece has at least one projection or groove, - a first rotating component on which the first insertion of the moveable shaft-piece is carried out, which has a housing with at least as many grooves or projections complementary to the surface shapes on the body of the moveable shaft-piece, as projections or grooves are in the moveable shaft-piece to insert into it, - a second rotating component of the system, second to be inserted into the moveable shaft-piece, which has a housing, characterised in that the housing of the second rotating component comprises at least as many grooves or projections complementary to the surface shapes on the body of the shaft-piece to be inserted into it, as projections or grooves in the body of the shaft-piece to be inserted into it, being staggered at an angle (α) with regard to the grooves or projections of the housing of the rotating component on which the first insertion of the shaft-piece is made, - and in that the grooves or projections of the housings (21, 23) of the rotating components (11, 12) coincide at least at one angle (α), being aligned and enabling the movement of the shaft-piece through the two components (11, 12) at the same time, and outside said angle (α) their movement is locked, both for attachment as well as disassembly, securing the attachment position of the shaft-piece, which cannot be removed. - at least one moveable shaft-piece, where this moveable shaft-piece has at least one projection or groove, - a first rotating component on which the first insertion of the moveable shaft-piece is carried out, which has a housing with at least as many grooves or projections complementary to the surface shapes on the body of the moveable shaft-piece, as projections or grooves are in the moveable shaft-piece to insert into it, - a second rotating component of the system, second to be inserted into the moveable shaft-piece, which has a housing, characterised in that the housing of the second rotating component comprises at least as many grooves or projections complementary to the surface shapes on the body of the shaft-piece to be inserted into it, as projections or grooves in the body of the shaft-piece to be inserted into it, being staggered at an angle (α) with regard to the grooves or projections of the housing of the rotating component on which the first insertion of the shaft-piece is made, - and in that the grooves or projections of the housings (21, 23) of the rotating components (11, 12) coincide at least at one angle (α), being aligned and enabling the movement of the shaft-piece through the two components (11, 12) at the same time, and outside said angle (α) their movement is locked, both for attachment as well as disassembly, securing the attachment position of the shaft-piece, which cannot be removed.