Elastic means for rolling up a roller curtain include a plurality of springs (26, 27, 28) fastened rigidly to a common support (15) connected to a shaft (2) and with respective support and constraint elements (36, 37, 38) which are geometrically coupled to the roller (19). A device for connecting the springs to a stationary frame (35) of the curtain (20) reduces the number of springs torsional turns with respect to the number of turns of the roller (19) by interposition of a speed reducer between the shaft (2), to which the springs are fastened, the stationary frame (35) and the roller (19). The shaft (2) end is located closer to the most external support and constraint element (36) and its extremity has a disc (11) mounted thereto. The coupling device together with the springs (50), their supports (15, 36, 37, 38), the shaft (2) and an external support cylindrical body (6) form a compact assembly, which is introduced into one head of the roller (19). The other head of the roller (19) features a cap (12), rotatably fastened to a cylindrical section of a support (13) which is locked to the stationary frame (35) by a tang (14). The geometrical coupling between the shaft (2) and the spring supports (15, 36, 37, 38) allows for easy and quick relocation of the roll up device on each side of the window to which the roller curtain is to be mounted.