A valve assembly has a housing with a first inlet, a second inlet, a first outlet, and a second outlet. A first flow path is between the first inlet and the first outlet, a second flow path is between the second inlet and the first outlet, and a third flow path is between the first inlet and the second outlet. A closure element is movably supported in the housing and in a by-pass position opens the first flow path and closes at least the second flow path, and in a normal position closes the first flow path and opens the second flow path and the third flow path. A flow guiding element is on the closure element, and which in the normal position protrudes into the second flow path and is coupled to the closure element to urge, in a gas flow from the second inlet to the first outlet, the closure element into the normal position. An exhaust gas system includes the valve assembly and an exhaust gas heat exchanger.