A system for fixing mounting rails, - with a first component which comprises an accommodating means, and with a second component which comprises an extension, wherein the extension may be fittingly inserted into the accommodating means for assembling the second component with the first component in such a manner that the second component is defined in three rotatory degrees of freedom (r1, r2, r3) and two translatory degrees of freedom (t1, t2) relative to the first component and is positioned in a first orientation, - and the second component may alternatively be assembly with the first component in a second orientation, wherein the first orientation and the second orientation differ from each other by a rotation of the second component about an axis through a right angle, - and with an adapter which comprises a U-shaped cross-section with extensions which diametrically protrude outwardly at its ends, wherein the adapter may be fittingly placed onto the second component in such a manner that the adapter is defined transversally and rotatorily relative to the axis, wherein the adapter and the second component are in mutual engagement, - and the second component in the second orientation may be assembled with the first component by means of the adapter, wherein the adapter may be fittingly inserted into the accommodating means in such a manner that the adapter is defined in the three rotatory degrees of freedom (r1, r2, r3) and the two translatory degrees of freedom (t1, t2) relative to the first component and the second component may be defined axially between the first component and the adapter relative to the axis. - with a first component which comprises an accommodating means, and with a second component which comprises an extension, wherein the extension may be fittingly inserted into the accommodating means for assembling the second component with the first component in such a manner that the second component is defined in three rotatory degrees of freedom (r1, r2, r3) and two translatory degrees of freedom (t1, t2) relative to the first component and is positioned in a first orientation, - and the second component may alternatively be assembly with the first component in a second orientation, wherein the first orientation and the second orientation differ from each other by a rotation of the second component about an axis through a right angle, - and with an adapter which comprises a U-shaped cross-section with extensions which diametrically protrude outwardly at its ends, wherein the adapter may be fittingly placed onto the second component in such a manner that the adapter is defined transversally and rotatorily relative to the axis, wherein the adapter and the second component are in mutual engagement, - and the second component in the second orientation may be assembled with the first component by means of the adapter, wherein the adapter may be fittingly inserted into the accommodating means in such a manner that the adapter is defined in the three rotatory degrees of freedom (r1, r2, r3) and the two translatory degrees of freedom (t1, t2) relative to the first component and the second component may be defined axially between the first component and the adapter relative to the axis.