The invention provides a process for preparing polyetheramines of the formula (1), R2 (NR1R3)n, in which n is a number from 1 to 20, R2 represents an organic radical that contains between 2 and 600 oxalkylene groups, and R1 and R3 are alike or different and represent hydrogen or an organic radical having 1 to 400 carbon atoms, by combining a compound of the formula (2), H(NR1R3), with a compound of the formula (3), R2 (OH)n, in the presence of hydrogen with a metal-containing catalyst whose metal content, based on the dry, reduced catalyst excluding any support material that may be present, is composed either of at least 80% by mass of cobalt or, in the case of Raney catalysts, of at least 80% by mass of metals from the group consisting of cobalt and aluminium, the catalyst containing less than 5% by mass of copper.