A process for the manufacture of alkoxylated derivatives of hydrogenated or (per)halogenated polymers comprising at least one -OH group [polymer (P ALK-OH)], said process comprising the steps of: (a) contacting at least one pre-catalyst [pre-catalyst C] complying with the following formula E t wherein E is an element selected from IV-group metals, post-transition metals and silicon, Q is chlorine, bromine, iodine or an optionally fluorinated alkoxy or aryloxy group, and t is an integer corresponding to the valence of E; with (a-i) at least one hydrogenated or (per)halogenated polymer comprising at least one -OH group [polymer (P OH)], thus providing a mixture [mixture (M a-1)] comprising said polymer P OH and a product [product (C-P OH)] obtained by the reaction between said pre-catalyst C and said polymer (P OH), or (a-ii) at least one source of iodine [compound I], thus providing a mixture [mixture (M a-2)] comprising said pre-catalyst C and said compound; (b) contacting said mixture (M a-1) with at least one source of iodine [compound I] or contacting said mixture (M a-2) with at least one polymer (P OH), thus obtaining mixture (M b) comprising said polymer (P OH), said product (C-P OH) and said compound; (c) contacting said mixture (M b) with at least one alkylene oxide, thus obtaining polymer (P ALK-OH), optionally in admixture [mixture (M c)] with said polymer (P OH), said product (C-P OH) and/or said compound. (a) contacting at least one pre-catalyst [pre-catalyst C] complying with the following formula E t wherein E is an element selected from IV-group metals, post-transition metals and silicon, Q is chlorine, bromine, iodine or an optionally fluorinated alkoxy or aryloxy group, and t is an integer corresponding to the valence of E; with (a-i) at least one hydrogenated or (per)halogenated polymer comprising at least one -OH group [polymer (P OH)], thus providing a mixture [mixture (M a-1)] comprising said polymer P OH and a product [product (C-P OH)] obtained by the reaction between said pre-catalyst C and said polymer (P OH), or (a-ii) at least one source of iodine [compound I], thus providing a mixture [mixture (M a-2)] comprising said pre-catalyst C and said compound; E is an element selected from IV-group metals, post-transition metals and silicon, Q is chlorine, bromine, iodine or an optionally fluorinated alkoxy or aryloxy group, and t is an integer corresponding to the valence of E; (a-i) at least one hydrogenated or (per)halogenated polymer comprising at least one -OH group [polymer (P OH)], thus providing a mixture [mixture (M a-1)] comprising said polymer P OH and a product [product (C-P OH)] obtained by the reaction between said pre-catalyst C and said polymer (P OH), or (a-ii) at least one source of iodine [compound I], thus providing a mixture [mixture (M a-2)] comprising said pre-catalyst C and said compound; (b) contacting said mixture (M a-1) with at least one source of iodine [compound I] or contacting said mixture (M a-2) with at least one polymer (P OH), thus obtaining mixture (M b) comprising said polymer (P OH), said product (C-P OH) and said compound; (c) contacting said mixture (M b) with at least one alkylene oxide, thus obtaining polymer (P ALK-OH), optionally in admixture [mixture (M c)] with said polymer (P OH), said product (C-P OH) and/or said compound.