A process is described for preparation of oxymethylene homo- and copolymers. This encompasses heterogeneous polymerization of a monomer which forms oxymethylene groups in the presence of an acetal of formaldehyde and of an initiator for cationic polymerization, followed by the deactivation of the polymer in a homogeneous phase via treatment with a basic aprotic solvent or with an aprotic solvent which comprises a base. Oxymethylene homopolymers with very high stability are also described.