Rotating machine comprising a shaft, a casing, at least one main magnetic bearing connected to the shaft for rotatably supporting said shaft inside the casing, at least one first and one second auxiliary rolling bearings (20, 22) positioned between the shaft and the casing to support axial and radial loads, said auxiliary rolling bearings each being provided with an inner ring (20a, 22a), with an outer ring (20b, 22b) and with at least one row of rolling elements positioned between the rings, first and second axial abutment means (44, 54) positioned on the shaft to transmit axial loads to the inner rings of the first and second rolling bearings, a spacer axially positioned between facing faces of the inner rings (20a, 22a) of said rolling bearings and mounted in axial contact with said faces for the transmission of the axial loads between said inner rings, and at least a first axial retaining means positioned on the casing and located axially between facing faces of the outer rings (20b, 22b) of the first and second rolling bearings for the transmission of the axial loads between at least one of said outer rings and the casing, characterized in that it further comprises: - second and third axial retaining means (48, 56) positioned on the casing to axially maintain the outer rings (20b, 22b) of the first and second rolling bearings, each of the second and third axial retaining means being located axially on the side opposite to the first axial retaining means with regard to associated rolling bearing, and - two pairs of first and second pre-stressing and damping elements (60, 62, 64, 66) each axially preloading one of the first and second rolling bearings, - the first pre-stressing and damping element of one of said pairs being axially positioned between the first axial retaining means and the outer ring of one of the first and second rolling bearings, the second pre-stressing and damping element of said pair being axially positioned between the second axial retaining means and said outer ring, an axial gap being provided between said first pre-stressing and damping element and the first axial retaining means, - the first pre-stressing and damping element of the other pair being axially positioned between the third axial retaining means and the outer ring of the other rolling bearing, the second pre-stressing and damping element of said other pair being axially positioned between the first axial retaining means and said outer ring, an axial gap being provided between said first pre-stressing and damping element and the third axial retaining means. - second and third axial retaining means (48, 56) positioned on the casing to axially maintain the outer rings (20b, 22b) of the first and second rolling bearings, each of the second and third axial retaining means being located axially on the side opposite to the first axial retaining means with regard to associated rolling bearing, and - two pairs of first and second pre-stressing and damping elements (60, 62, 64, 66) each axially preloading one of the first and second rolling bearings, - the first pre-stressing and damping element of one of said pairs being axially positioned between the first axial retaining means and the outer ring of one of the first and second rolling bearings, the second pre-stressing and damping element of said pair being axially positioned between the second axial retaining means and said outer ring, an axial gap being provided between said first pre-stressing and damping element and the first axial retaining means, - the first pre-stressing and damping element of the other pair being axially positioned between the third axial retaining means and the outer ring of the other rolling bearing, the second pre-stressing and damping element of said other pair being axially positioned between the first axial retaining means and said outer ring, an axial gap being provided between said first pre-stressing and damping element and the third axial retaining means.