A mechanical seal arrangement comprising - a mechanical seal having a rotating slide ring and a stationary slide ring defining a seal gap therebetween, - a secondary seal arranged on a back side of one of the slide rings facing away from a sliding surface of the slide ring, - the secondary seal being made of a base material and having a coating such that a substance-to-substance bond is formed between the coating and the base material of the secondary seal, - a sleeve-shaped component which is arranged radially inside the secondary seal, a gap having a gap height being present between the sleeve-shaped component and a region of one of the slide rings facing radially inwards, the secondary seal sealing against the back side of this slide ring and the sleeve-shaped component - wherein the coating is provided on a first side of the secondary seal facing the slide ring and a second side of the secondary seal facing the sleeve-shaped component, - wherein a stiffness of the coating is greater than a stiffness of the base material of the secondary seal, - wherein a thickness of the coating is smaller than or equal to a gap height of the gap, - wherein the coating on the first side of the secondary seal is provided only partially, - wherein the coating on the second side of the secondary seal is provided only partially, and - wherein the base material of the secondary seal at the uncoated region of the first side bears directly against the rear side of the stationary slide ring and wherein the base material of the secondary seal at the uncoated region of the second side bears directly against the sleeve-shaped component. - a mechanical seal having a rotating slide ring and a stationary slide ring defining a seal gap therebetween, - a secondary seal arranged on a back side of one of the slide rings facing away from a sliding surface of the slide ring, - the secondary seal being made of a base material and having a coating such that a substance-to-substance bond is formed between the coating and the base material of the secondary seal, - a sleeve-shaped component which is arranged radially inside the secondary seal, a gap having a gap height being present between the sleeve-shaped component and a region of one of the slide rings facing radially inwards, the secondary seal sealing against the back side of this slide ring and the sleeve-shaped component - wherein the coating is provided on a first side of the secondary seal facing the slide ring and a second side of the secondary seal facing the sleeve-shaped component, - wherein a stiffness of the coating is greater than a stiffness of the base material of the secondary seal, - wherein a thickness of the coating is smaller than or equal to a gap height of the gap, - wherein the coating on the first side of the secondary seal is provided only partially, - wherein the coating on the second side of the secondary seal is provided only partially, and - wherein the base material of the secondary seal at the uncoated region of the first side bears directly against the rear side of the stationary slide ring and wherein the base material of the secondary seal at the uncoated region of the second side bears directly against the sleeve-shaped component.