Polyglycerols obtained by polymerizing glycerine with the aid of an alkaline catalyst at a temperature below 260 DEG C. in a non-oxidizing atmosphere, preferably at subatmospheric pressure, are (a) esterified with a monobasic acid or an anhydride or halide of such an acid, or with a mixture of such acids, anhydrides or halides, or (b) re-esterified with a triglyceride of a monobasic acid, or a mixture of such triglycerides; the esterification or re-esterification is effected at below 250 DEG C. in a non-oxidizing atmosphere in the presence of an alkaline catalyst, preferably at subatmospheric pressure, and the proportions are such that the products contain at least one unesterified hydroxy group. In examples of the preparation of polyglycerols: (1) glycerol is heated to 225--230 DEG C. with 1 per cent of caustic soda under a reflux condenser kept at about 100 DEG C. and with a stream of carbon dioxide passing through the mixture; a product of molecular weight 166 is obtained; (2) the same mixture as in example 1 is heated in carbon dioxide to 220--225 DEG C. while the pressure is reduced in stages to 70 mm., this yielding a product of molecular weight 256; (3) the product of example 1 is freed from unpolymerized glycerol by distillation at 235 DEG C. and 2--5 mm. pressure with a stream of inert gas bubbled through the liquid. Other alkaline catalysts which may be used are sodium carbonate and bicarbonate, other alkali carbonates and hydroxides, oxides of calcium, magnesium and zinc, trisodium phosphate and sodium tetraborate. In examples of the esterification of polyglycerols, (4) the product of example 3, still containing the alkaline catalyst, is heated to 220--230 DEG C. with oleic and stearic acids in an atmosphere of carbon dioxide; (5) the product of example 3 is heated to 205 DEG C. under 35--50 mm. pressure with the acids of hydrogenated cottonseed oil in an atmosphere of nitrogen. Other specified acids which may be used are acetic, propionic, butyric, valeric, caprylic, caproic, capric, lauric, myristic, palmitic, ricinoleic, hydroxystearic, behenic, linoleic, linolenic, naphthenic, benzenesulphonic, naphthalenesulphonic, cetylsulphonic, dodecylsulphonic, benzoic and naphthoic acids, and the acids derived from coconut oil, palm-kernel oil, tallow, oleo oil, oleostearine, palm oil, cottonseed oil, soy oil, corn oil, sunflower oil, sesame oil, linseed oil, whale oils, fish oils, lard and rosin, and their hydrogenation products; the specified oils and fats may be used also in the re-esterification process. The polyglycerols and their esters may be improved in odour and taste by steam treatment at atmospheric or reduced pressure. The esters are useful as antispattering additions to margarine, as emulsifying agents, particularly in edible emulsions such as cake batters and shortenings, and also as wetting agents. Specification 421,284 is referred to. The Specification as open to inspection under Sect. 91 includes four further examples of the preparation of polyglycerols, generally similar to examples 1 and 2 above, in which products of molecular weights 148--163, 326, 179, and 207 are obtained. Sodium acetate, iodine and zinc chloride are additional specified catalysts for use in the production of polyglycerols. The Specification also includes two further examples, generally similar to example 3 above, of the removal of glycerol from polyglycerols by distillation, products of the molecular weights 205 and 345 being obtained. An example in which a polyglycerol is refined by steam treatment at 180--200 DEG C. and 50--20 mm. pressure is also included, as well as two additional esterification examples in which (1) a polyglycerol of molecular weight 256 is esterified with stearic acid, substantially as in example 4 above and (2) the polyglycerol stearate so obtained is heated again under similar conditions with stearic acid. This subject-matter does not appear in the Specification as accepted.ALSO:Polyglycerols are (a) esterified with a monobasic acid or an anhydride or halide of such an acid, or with a mixture of such acids, anhydrides or halides, or (b) re-esterified with a triglyceride of a monobasic acid, or a mixture of such triglycerides; the proportions are such that the products contain at least one unesterified hydroxy group. Examples are given in which a polyglycerol is esterified with a mixture of oleic and stearic acids and with the acids of hydrogenated cottonseed oil. Other specified acids which may be used are acetic, propionic, butyric, valeric, caprylic, caproic, capric, lauric, myristic, palmitic, ricinoleic, hydroxystearic, behenic, linoleic, linolenic, naphthenic, benzenesulphonic, naphthalenesulphonic, cetylsulphonic, dodecylsulphonic, benzoic and naphthoic acids, and the acids derived from coconut oil, palm-kernel oil, tallow, oleo oil, oleostearine, palm oil, cottonseed oil, soy oil, corn oil, sunflower oil, sesame oil, linseed oil, whale oils, fish oils, lard and rosin, and their hydrogenation products; the specified oils and fats may be used also in the re-esterification process. The esters are useful as emulsifying agents, particularly in edible emulsions such as cake batters and shortenings. Specification 421,284, [Group IV], is referred to. The Specification as open to inspection under Sect. 91 includes two additional examples in which (1) a polyglycerol of molecular weight 256 is esterified with stearic acid, and (2) the polyglycerol stearate so obtained is heated again under similar conditions with stearic acid. This subject-matter does not appear in the Specification as accepted.ALSO:Polyglycerols are (a) esterified with a monobasic acid or an anhydride or halide of such an acid, or with a mixture of such acids, anhydrides or halides, or (b) re-esterified with a triglyceride of a monobasic acid, or a mixture of such triglycerides. Examples are given in which a polyglycerol is esterified with a mixture of oleic and stearic acids and with the acids of hydrogenated cottonseed oil. Other specified acids which may be used are acetic, propionic, butyric, valeric, caprylic, caproic, capric, lauric, myristic, palmitic, ricinoleic, hydroxystearic, behenic, linoleic, linolenic, naphthenic, benzenesulphonic, naphthalenesulphonic, cetylsulphonic, dodecylsulphonic, benzoic and naphthoic acids, and the acids derived from coconut oil, palm-kernel oil, tallow, oleo oil, oleostearine, palm oil, cottonseed oil, soy oil, corn oil, sunflower oil, sesame oil, linseed oil, whale oils, fish oils, lard and rosin, and their hydrogenation products; the specified oils and fats may be used also in the re-esterification process. The esters may be improved in odour and taste by steam treatment at atmospheric or reduced pressure. They are useful as antispattering additions to margarine. Specification 421,284, [Group IV], is referred to. The Specification as open to inspection under Sect. 91 includes two additional examples in which (1) a polyglycerol of molecular weight 256 is esterified with stearic acid, and (2) the polyglycerol stearate so obtained is heated again under similar conditions with stearic acid. This subject-matter does not appear in the Specification as accepted.