A process for the continuous separation of methanol and water from a feed mixture containing predominantly tetrahydrofuran admixed with water, methanol and small amounts of additional compounds, in a rectifying apparatus having at last two rectifying columns, of which two are operated at different pressures which involves feeding the raw material into a first column operated under lower pressure, and introducing the distillate from the column operated under a lower pressure to a second column operated under a higher pressure, while a product stream from the second column operated under a higher pressure is reintroduced into the first column operated under a lower pressure. In this process the product stream withdrawn from the second column operated under a higher pressure is withdrawn as a side stream from the stripping or enrichment section of the second column and is returned into the first column operated under a lower pressure, while a methanol-enriched product stream containing practically all of the methanol introduced with the raw material into the rectifying apparatus is withdrawn from the head of the second column operated under a higher pressure. The first column is operated for example at atmospheric pressure and the second column is operated at a pressure of from 1 to 25 bar.