Backrest of a vehicle seat, said backrest comprising a frame and a lumbar supporting device comprising: - a supporting member attached to said frame and defining a rear surface and a front surface, which is shaped to support a portion of a user's back; - a Bowden cable adjustment assembly for adjusting the shape and/or position of said front surface; said assembly comprising: a) at least one sheath having one end connected to a first element defined by one of either said frame or said rear surface; b) two wire sections arranged outside said sheath and having respective ends connected to a second element defined by the other of either said frame or said rear surface; c) a control device that can be operated by the user to pull/release said wire sections with respect to said sheath; - connecting means to movably connect the end of said sheath to said first element and/or the ends of said wire sections to said second element; characterized in that said connecting means: - give a freedom of movement to the end of said sheath in relation to said first element and/or to the ends of said wire sections in relation to said second element starting from a reference position, such as to enable said supporting member to move backwards, in use, in response to a longitudinal inertial force acting against said front surface, and - comprise retaining means to hold, in said reference position, the end of said sheath in relation to said first element and/or the ends of said wire sections in relation to said second element until said longitudinal inertial force exceeds a previously defined threshold value. - a supporting member attached to said frame and defining a rear surface and a front surface, which is shaped to support a portion of a user's back; - a Bowden cable adjustment assembly for adjusting the shape and/or position of said front surface; said assembly comprising: a) at least one sheath having one end connected to a first element defined by one of either said frame or said rear surface; b) two wire sections arranged outside said sheath and having respective ends connected to a second element defined by the other of either said frame or said rear surface; c) a control device that can be operated by the user to pull/release said wire sections with respect to said sheath; a) at least one sheath having one end connected to a first element defined by one of either said frame or said rear surface; b) two wire sections arranged outside said sheath and having respective ends connected to a second element defined by the other of either said frame or said rear surface; c) a control device that can be operated by the user to pull/release said wire sections with respect to said sheath; - connecting means to movably connect the end of said sheath to said first element and/or the ends of said wire sections to said second element; - give a freedom of movement to the end of said sheath in relation to said first element and/or to the ends of said wire sections in relation to said second element starting from a reference position, such as to enable said supporting member to move backwards, in use, in response to a longitudinal inertial force acting against said front surface, and - comprise retaining means to hold, in said reference position, the end of said sheath in relation to said first element and/or the ends of said wire sections in relation to said second element until said longitudinal inertial force exceeds a previously defined threshold value.