A process for the formation of a graphene membrane component includes arranging a graphene membrane in a relaxed condition of the graphene membrane on a surface of a supportive substrate. The graphene membrane extends across a cut-out with an opening at the surface of the supportive substrate. The graphene membrane is moreover arranged so that a first portion of the graphene membrane is arranged on the surface of the supportive substrate and a second portion of the graphene membrane is arranged over the opening of the cut-out. The process further includes tensioning of the second portion of the graphene membrane, in order to convert the second portion of the graphene membrane to a tensioned condition, so that the second portion of the graphene membrane is permanently in the tensioned condition in an operating temperature range of the graphene membrane component.