A pneumatic support, in particular for a machine, being interposed between and secured to a first part such as a carrier structure and a second part such as a driving device, such that: - a first rigid carrier means is able to provide the rigid association of the pneumatic support with one of the two parts, comprises a lateral wall portion and a transverse wall portion and a second rigid carrier means is able to provide the rigid association of the pneumatic support with the other part, - a first spring means, comprising an elastomer material, is interposed between and rigidly secured towards its lateral periphery with the lateral wall portion and towards this median periphery with the second carrier means, and has a median transverse face directed towards the transverse wall portion, - a second spring means, comprising an elastomer material, is rigidly secured towards its lateral periphery to the lateral wall portion, and has a median transverse face and an opposite transverse face, - the two median transverse faces (16, 19) of the first and second spring means (4, 5) are facing each other and form a first deformable working chamber, while the opposite transverse face and the transverse wall portion are facing each other and form a second chamber, - a first hole provides communication between the first working chamber and the external atmosphere and a second hole provided in the transverse wall portion provides communication between the second chamber and the external atmosphere, characterised in that: - a second spring means has low rigidity and has, between its median transverse face and the opposite transverse face, roughly flat, has an overall thickness that varies by no more than the ratio 1 to 2, and, at rest, said median transverse face is separated from the median transverse face of the first spring means, while the opposite transverse face is separated from the internal face of the transverse wall portion, - in the case of dynamic deformation of the second spring means with an amplitude less than a lower bound, said median transverse face is in a free state in which it is separated from the median transverse face of the first spring means, while the opposite transverse face is in a free state in which it is separated from the internal face of the transverse wall portion, - in the case of dynamic deformation lying between the lower bound and an upper bound, said median transverse face is in a secured state in which it is in abutment contact with the median transverse face of the first spring means, while the opposite transverse face is in the free state, - in the case of dynamic deformation higher than the upper bound, said median transverse face is in the secured state and the opposite transverse face is in a secured state in which it is in abutment contact with the internal face of the transverse wall portion. - a first rigid carrier means is able to provide the rigid association of the pneumatic support with one of the two parts, comprises a lateral wall portion and a transverse wall portion and a second rigid carrier means is able to provide the rigid association of the pneumatic support with the other part, - a first spring means, comprising an elastomer material, is interposed between and rigidly secured towards its lateral periphery with the lateral wall portion and towards this median periphery with the second carrier means, and has a median transverse face directed towards the transverse wall portion, - a second spring means, comprising an elastomer material, is rigidly secured towards its lateral periphery to the lateral wall portion, and has a median transverse face and an opposite transverse face, - the two median transverse faces (16, 19) of the first and second spring means (4, 5) are facing each other and form a first deformable working chamber, while the opposite transverse face and the transverse wall portion are facing each other and form a second chamber, - a first hole provides communication between the first working chamber and the external atmosphere and a second hole provided in the transverse wall portion provides communication between the second chamber and the external atmosphere, - a second spring means has low rigidity and has, between its median transverse face and the opposite transverse face, roughly flat, has an overall thickness that varies by no more than the ratio 1 to 2, and, at rest, said median transverse face is separated from the median transverse face of the first spring means, while the opposite transverse face is separated from the internal face of the transverse wall portion, - in the case of dynamic deformation of the second spring means with an amplitude less than a lower bound, said median transverse face is in a free state in which it is separated from the median transverse face of the first spring means, while the opposite transverse face is in a free state in which it is separated from the internal face of the transverse wall portion, - in the case of dynamic deformation lying between the lower bound and an upper bound, said median transverse face is in a secured state in which it is in abutment contact with the median transverse face of the first spring means, while the opposite transverse face is in the free state, - in the case of dynamic deformation higher than the upper bound, said median transverse face is in the secured state and the opposite transverse face is in a secured state in which it is in abutment contact with the internal face of the transverse wall portion.