TECHNOLOGY FOCUS - INSTRUMENTATION AND TESTING - Preferred Components: The dimethyl ether purification stage downstream the dimethyl ether reactor is connected with at least one methanol final purification stage via a methanol re-circulating line. The methanol preliminary purification and/or the methanol final purification exhibit at least one distillation column (2). The methanol final purification comprises two distillation columns, one of which is operated under the elevated pressure, and the other is operated under the atmospheric pressure. A re-circulating line from the top of the dimethyl ether purification column is connected to at least one purification device, preferably a washing column. At least one stage of the methanol final purification is connected with a feeding line of the dimethyl ether reactor.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Method: The preliminary purification of methanol, the final purification of methanol and/or the purification of dimethyl ether take place by distillation. The purification of methanol is carried out in a first column, which is operated under an elevated pressure, and/or a second column, which is operated under an atmospheric pressure. The removed methanol flow from the dimethyl ether purification stage is fed at least partially into a pressure column (50) and/or an atmospheric column (70). Dimethyl ether is recovered by purifying, preferably by washing the gaseous top product of dimethyl ether with a methanol-rich detergent. The methanol stream is fed for converting at least a partial flow of methanol into dimethyl ether after at least one of the final purification stage. The division of methanol flow into the methanol final purification and the dimethyl ether production takes place after the pressure column. The gaseous top product of the pressure column is fed at least partially into the dimethyl ether reactor. The top product of the pressure column is compressed before introducing into the dimethyl ether reactor. EXAMPLE - No suitable example given.