A flange connection has two flanges and a weld ring gasket arranged between the flanges, wherein the weld ring gasket has two weld ring halves arranged one on top of the other, each having a base section and a lip arranged on it, wherein the weld ring halves are welded to the base section by way of a fillet weld with the flange that lies against it, and wherein the lips form a torus-shaped connection section having a hollow interior, and the weld ring halves are welded to one another at the torus-shaped connection section, by way of a caulking seam. The torus-shaped connection section is arranged to lie radially on the inside.