In order, in a particularly simple way, to allow multiple separation and connection of line sections of a line, through which a hot and highly compressed medium flows, in particular a pipeline, through which steam flows, there is provided a double-walled flanged connection. The double-walled flange connection is formed of an outer flange and an inner flange, between which an interspace, through which a cooling medium is capable of flowing, is formed. The apparatus is particularly suitable for the connection of line sections of a steam turbine.