In the production of purified methanol and/or dimethyl ether from crude methanol, the crude methanol is processed in at least one prepurification stage, a first partial stream of the prepurified methanol is supplied to a final methanol purification and a second partial stream of the prepurified methanol is supplied to a reactor and at least partly converted to dimethyl ether. The dimethyl ether recovered is purified in at least one purification stage, wherein non-reacted methanol is withdrawn from the dimethyl ether purification stage and at least partly supplied to the final methanol purification. In this way, both purified methanol and dimethyl ether can be produced in parallel, wherein the quantities of both products obtained are flexibly adjustable.