A process for preparing polyoxymethylene homopolymers or copolymers by homopolymerization or copolymerization of trioxane or additionally of suitable comonomers, in which trioxane which still comprises residual monomers is firstly prepared in a monomer plant and is degassed in one or more stages to give one or more vapor streams (13, 14) which are, if appropriate, fed to a condenser (K) in which the condensable fractions of these vapor streams are condensed to give a condensate (15) which is recycled to the polymerization reactor (P) and one or more gaseous, formaldehyde-comprising streams (16) and also a partially degassed polyoxymethylene homopolymer or copolymer (17) which is fed to an extruder (E) or kneader and is mixed with customary additives and processing aids in this to give a polymer melt (19) and extraction of a formaldehyde-comprising extruder or kneader offgas (18) from the extruder (E) or kneader, wherein the formaldehyde-comprising secondary streams (14, 16, 18) from the polymer plant are recycled directly without addition of auxiliaries to the monomer plant, is proposed