Polymeric trimethylene oxide alcohols with polyether side chains having the general formula: <FORM:0789415/IV (b)/1> wherein X and Y are equal to or greater than 1, Z is more than 1 and R is H, OH, alkyl, or hydroxyalkyl or is: <FORM:0789415/IV (b)/2> are stated to be applicable as levelling agents in dyeing. According to Example (12), for the preparation of textile dyeings which are uniform in shade and penetration, a 0.4 per cent bath of a dimethoxyviolanthrene dyestuff is mixed with a polymeric trimethylene oxide alcohol reacted with 6.8 mol. of ethylene oxide per hydroxyl group of the trimethylene oxide alcohol, 1.5-2 g. of the product being used per litre dye bath.  The polymeric trimethylene oxide alcohols can also be used with substantive or acid dyestuffs.  Specifications 787,669, [Group IX], and 787,922, [Group IV (b)], are referred to.ALSO:Polymeric trimethylene oxide alcohols with polyether side chains having the general formula <FORM:0789415/III/1> wherein X and Y are equal to or greater than 1, Z is more than 1 and R is hydroxyl, hydrogen, alkyl, or hydroxyalkyl, or is <FORM:0789415/III/2> are stated to be applicable as emulsifying agents or as cleansing agents. According to Example 10, mineral oil is emulsified with water, employing such a polyether as the emulsifying agent. According to Example 14, crepe paper is impregnated with a solution of such a polyether in methanol.  After evaporation of solvent the paper has absorbed about 50 per cent of the polyether, and with this paper panes of glass soiled by oil can be quickly cleaned.  Specifications 787,669, [Group IX], and 787,922, [Group IV (b)], are referred to.ALSO:Polymeric trimethylene oxide derivatives with polyether side chains which are water-soluble and have surface-active properties combined with antistatic effects and are thus suitable for use as auxiliaries in textile and paper dyeing, as wetting, emulsifying, dispersing and cleansing agents and as additives for pharmaceutical and cosmetic preparations are obtained by (a) polymerizing a trimethylene oxide alcohol of formula <FORM:0789415/IV (a)/1> and reacting the product with an alkylene oxide, or (b) reacting the alcohol and the alkylene oxide and polymerizing the product. Trimethylene alcohols specified are 3-ethyl, 3-methylol-, 3,3-dimethylol-trimethylene oxide, which may be prepared as described in Specifications 787,669, [Group IX], and 778,922, [Group IV (b)]. Ethylene oxide and propylene oxide are specified as alkylene oxides. Acid catalysts are employed, e.g. hypochlorous, sulphuric, phosphoric acids or cation exchangers, e.g. sulphonated styrene-divynyl benzene mixed polymers; Friedel-Crafts-type catalysts; the polymerization is effected at from room temperatures to 100 DEG  C. and the polymer is recovered by neutralizing the catalyst washing and filtering.  Mixed polymers may be obtained and the products may be esterified or etherified: (1) 3 gs. sodium are dissolved in 290 gs. (2.5 mol.) 3-ethyl-3-methylol trimethylene oxide and after blowing through the apparatus with nitrogen a stream of ethylene oxide is passed through at 130-135 DEG  C.  After 5 hours the 6.9 mol. of ethylene oxide have been absorbed and the product is then polymerized in presence of boron trifluoride etherate in benzene for 8 hours at 80 DEG  C. After neutralization of catalyst a light brown viscous paste is obtained soluble in chlorobenzene methylol, acetic esters and chloroform; (2) the product obtained in the first stage as in (1) is further reacted with more 3-ethyl-3-methylol trimethylene oxide in presence of the boron trifluoride catalyst; (3) 100 parts of the alcohol are reacted with 0.15 parts by volume of hypochlorous acid at 60 DEG  C. and the polymer neutralized with ammonia.  The volatiles are ditilled off to give a colourless hard resin having a 117 softening point.ALSO:Polymeric trimethyleneoxide alcohols with polyether side chains of the general formula <FORM:0789415/VI/1> p wherein X and Y are equal to or greater than 1; Z is more than 1; and R is H, OH, alkyl, hydroxylalkyl, or <FORM:0789415/VI/2> (see Group IV (a)) wherein X and Y are as above, are stated to be additives for pharmaceutical and cosmetic preparations, e.g. salves. Specifications 787,669, [Group IX], and 787,922, [Group IV (b)], are referred to.