A device for connection of a motor-vehicle component to the structure of a motor vehicle, - wherein said component comprises a main body provided with attachments for connection to the structure of the motor vehicle and an additional body connected to said main body; and - wherein said connection device comprises a connection flange associated to said additional body and a main connection screw for fixing said additional body to a respective supporting member forming part of the supporting structure of the motor vehicle or rigidly connected thereto, said connection device being characterized in that: - said connection flange has an eyelet for engagement of said main connection screw, said eyelet extending in a first direction; - said main connection screw is engaged with play through said eyelet of said connection flange and has a threaded end portion screwed within a threaded hole of said supporting member, said screw being oriented in a second direction orthogonal to said first direction; - arranged between said connection flange and said supporting member is a first arm of an L-shaped bracket; - said first arm of the L-shaped bracket has a hole traversed with play by said main connection screw; - said L-shaped bracket has a second arm orthogonal to the first arm and having an eyelet, which extends in a third direction orthogonal to said first direction of the eyelet of said connection flange, and to said second direction of said main connection screw; and - engaged within the eyelet of said second arm of the L-shaped bracket is an auxiliary locking screw, oriented in said first direction and having a threaded end portion screwed within a threaded hole formed in a side wall of said connection flange. - wherein said component comprises a main body provided with attachments for connection to the structure of the motor vehicle and an additional body connected to said main body; and - wherein said connection device comprises a connection flange associated to said additional body and a main connection screw for fixing said additional body to a respective supporting member forming part of the supporting structure of the motor vehicle or rigidly connected thereto, - said connection flange has an eyelet for engagement of said main connection screw, said eyelet extending in a first direction; - said main connection screw is engaged with play through said eyelet of said connection flange and has a threaded end portion screwed within a threaded hole of said supporting member, said screw being oriented in a second direction orthogonal to said first direction; - arranged between said connection flange and said supporting member is a first arm of an L-shaped bracket; - said first arm of the L-shaped bracket has a hole traversed with play by said main connection screw; - said L-shaped bracket has a second arm orthogonal to the first arm and having an eyelet, which extends in a third direction orthogonal to said first direction of the eyelet of said connection flange, and to said second direction of said main connection screw; and - engaged within the eyelet of said second arm of the L-shaped bracket is an auxiliary locking screw, oriented in said first direction and having a threaded end portion screwed within a threaded hole formed in a side wall of said connection flange.