The invention concerns polyesters of at least one of polyhydroxylated compounds at least partly acylated, belonging the group consisting of polyhydroxylated compounds constituted by glycerol polycarbonates, specific polyglycerols, [(a-hydroxymethyl) oxyethylene/(a-hydroxymethyl) ethylene carbonate] copolymers, [(a-hydroxymethyl) oxyethylene/(a-hydroxymethyl) ethylene carbonate] copolymers, [(a-alkyl) oxyethylene/(a-hydroxyalkyl) oxyethylene] copolymers. The invention also concerns a method for acylating at least partly one of said polyhydroxylated compounds. The invention is applicable to the technical fields relating to engine and industrial lubricants, greases, hydraulic fluids, metal deformation and processing lubricants, stripping and mold dressing products, oil prospecting, mines, tunnel borers, cosmetics, detergency, inks, textile coatings and papers, to the field of food products, to the protection of wood as synthesis intermediates.