An apparatus for compacting a continuous textile substrate by means of an endless elastic belt, comprising: - a heatable rotating cylinder; - said endless belt movable along a closed path to support and transport the continuous textile substrate in contact with a side surface portion of said heatable rotating cylinder, said belt being elastically deformable in elongation; - a roller system (31, 32, 33, 34, 35) on which said belt is wound in an elongation pretensioning state, wherein said roller system comprises a plurality of idle return rollers (33, 34, 35) and a plurality of motorized rollers (31, 32) operable so as to make said belt to slide along said closed path imposing on said belt an additional elongation tension state at a first section of said path extending - with respect to a direction of advancement of the belt - upstream of a second section of said path in which said belt is maintained in contact with the heatable rotating cylinder; - means for guiding said continuous textile substrate between said belt and said heatable rotating cylinder along said second section of said path, wherein the apparatus comprises a system for reducing friction coefficient between the belt and the heatable rotating cylinder, said system for reducing friction coefficient comprising one or more interposition tapes (61, 62) that: - are guided in partial winding around said heatable rotating cylinder and in direct contact with its side surface to interpose themselves between said belt and the side surface of said heatable rotating cylinder along said second section of the closed path of the belt at least at two axial end strips (11, 12) of the side surface of said heatable rotating cylinder that are in axially opposite positions with respect to the axis of rotation of said heatable rotating cylinder; and - are made of a material that is suitable to generate with the side surface of the heatable rotating cylinder a friction coefficient lower than that generated with the belt characterized in that said system for reducing friction coefficient comprises two distinct interposition tapes (61, 62) that are guided in partial winding around said heatable rotating cylinder and in direct contact with its side surface to interpose themselves between said belt and the side surface of said heatable rotating cylinder along said second section of the closed path of the belt and wherein a first interposition tape is guided at a first axial end strip of the side surface of said heatable rotating cylinder and a second interposition tape is guided at a second axial end strip of the side surface of said heatable rotating cylinder, said two interposition tapes (61, 62) leaving uncovered a central strip of the side surface of the heatable rotating cylinder to allow in use a continuous textile substrate to be treated to slide in direct contact with the heatable rotating cylinder. - a heatable rotating cylinder; - said endless belt movable along a closed path to support and transport the continuous textile substrate in contact with a side surface portion of said heatable rotating cylinder, said belt being elastically deformable in elongation; - a roller system (31, 32, 33, 34, 35) on which said belt is wound in an elongation pretensioning state, wherein said roller system comprises a plurality of idle return rollers (33, 34, 35) and a plurality of motorized rollers (31, 32) operable so as to make said belt to slide along said closed path imposing on said belt an additional elongation tension state at a first section of said path extending - with respect to a direction of advancement of the belt - upstream of a second section of said path in which said belt is maintained in contact with the heatable rotating cylinder; - means for guiding said continuous textile substrate between said belt and said heatable rotating cylinder along said second section of said path, - are guided in partial winding around said heatable rotating cylinder and in direct contact with its side surface to interpose themselves between said belt and the side surface of said heatable rotating cylinder along said second section of the closed path of the belt at least at two axial end strips (11, 12) of the side surface of said heatable rotating cylinder that are in axially opposite positions with respect to the axis of rotation of said heatable rotating cylinder; and - are made of a material that is suitable to generate with the side surface of the heatable rotating cylinder a friction coefficient lower than that generated with the belt characterized in that said system for reducing friction coefficient comprises two distinct interposition tapes (61, 62) that are guided in partial winding around said heatable rotating cylinder and in direct contact with its side surface to interpose themselves between said belt and the side surface of said heatable rotating cylinder along said second section of the closed path of the belt and wherein a first interposition tape is guided at a first axial end strip of the side surface of said heatable rotating cylinder and a second interposition tape is guided at a second axial end strip of the side surface of said heatable rotating cylinder, said two interposition tapes (61, 62) leaving uncovered a central strip of the side surface of the heatable rotating cylinder to allow in use a continuous textile substrate to be treated to slide in direct contact with the heatable rotating cylinder.