Self-closing device for sliding doors, said doors being of the type which comprise at least one sliding leaf which is hung from an upper profile and configured to be displaced in the direction thereof, comprising: • a drive belt arranged along the upper profile; • a closing pulley, provided with elastic means, that is arranged on a first rotation axis integral to the upper profile and that engages with a first end of the drive belt, where said pulley is configured to: ∘ load the elastic means during the opening of the sliding leaf; and to ∘ push the sliding leaf during the closing thereof through the rotation movement in the opposite direction that transmits the unloading of the elastic means; and; • a brake pulley, provided with stopping means, which is arranged on a second rotation axis integral to the upper profile and which engages with a second end of the drive belt opposite to the first end, the rotation movement of both pulleys (20, 40) being connected by the drive belt, where said brake pulley is configured to: ∘ disengage the stopping means during the opening of the sliding leaf, and to ∘ stop the sliding leaf during the closing thereof by means of a clutch of the stopping means; said device being characterized in that the drive belt is configured to be joined to the sliding leaf and to load the elastic means through the rotation movement transmitted by said drive belt; and in that the brake pulley is provided with a stop body, joined to the second rotation axis by means of a third bearing, that has an inner housing configured to house said stopping means and with a brake cap that has second fastening means to the stop body to contain the stopping means; said stopping means comprising: - a friction brake drum joined to the stop body by means of third fastening means; and - a brake shaft joined to the second rotation axis by means of a unidirectional bearing, which is freely coupled to the brake drum, where said unidirectional bearing is configured to: ∘ allow the rotation movement of the brake shaft during the opening of the sliding leaf, so that said shaft rotates at the same speed and in the same direction as the brake drum, preventing any friction between them; and ∘ block the rotation movement of the brake shaft in the opposite direction during the closing of the sliding leaf, so that said shaft does not move and produces friction against the brake drum. • a drive belt arranged along the upper profile; • a closing pulley, provided with elastic means, that is arranged on a first rotation axis integral to the upper profile and that engages with a first end of the drive belt, where said pulley is configured to: ∘ load the elastic means during the opening of the sliding leaf; and to ∘ push the sliding leaf during the closing thereof through the rotation movement in the opposite direction that transmits the unloading of the elastic means; and; ∘ load the elastic means during the opening of the sliding leaf; and to ∘ push the sliding leaf during the closing thereof through the rotation movement in the opposite direction that transmits the unloading of the elastic means; and; • a brake pulley, provided with stopping means, which is arranged on a second rotation axis integral to the upper profile and which engages with a second end of the drive belt opposite to the first end, the rotation movement of both pulleys (20, 40) being connected by the drive belt, where said brake pulley is configured to: ∘ disengage the stopping means during the opening of the sliding leaf, and to ∘ stop the sliding leaf during the closing thereof by means of a clutch of the stopping means; ∘ disengage the stopping means during the opening of the sliding leaf, and to ∘ stop the sliding leaf during the closing thereof by means of a clutch of the stopping means; - a friction brake drum joined to the stop body by means of third fastening means; and - a brake shaft joined to the second rotation axis by means of a unidirectional bearing, which is freely coupled to the brake drum, where said unidirectional bearing is configured to: ∘ allow the rotation movement of the brake shaft during the opening of the sliding leaf, so that said shaft rotates at the same speed and in the same direction as the brake drum, preventing any friction between them; and ∘ block the rotation movement of the brake shaft in the opposite direction during the closing of the sliding leaf, so that said shaft does not move and produces friction against the brake drum. ∘ allow the rotation movement of the brake shaft during the opening of the sliding leaf, so that said shaft rotates at the same speed and in the same direction as the brake drum, preventing any friction between them; and ∘ block the rotation movement of the brake shaft in the opposite direction during the closing of the sliding leaf, so that said shaft does not move and produces friction against the brake drum.