A continuous process for the preparation of amphiphilic graft polymers, wherein a vinyl ester component (B) composed of vinyl acetate and/or vinyl propionate (B1) and, optionally, a further ethylenically unsaturated monomer (B2), is polymerized in the presence of a polyalkylene oxide (A), a free radical-forming initiator (C) and, optionally, an additive (D), at a mean polymerization temperature at which the initiator (C) has a decomposition half-time of from 1 to 500 min, in at least one tubular reactor segment with a feed side and an outlet side, through which the reaction mixture comprising at least a part of component (A) to (C), and optionally (D), streams.