Complex esters of a polyhydric alcohol with an a -g -diolefinic carboxylic acid and another carboxylic acid not containing an additional functional group (such as -OH, NH2 or NH) are made by reacting the polyhydric alcohol with the acids or hydrolyzable derivatives thereof in any order. The polyhydric alcohol may be glycerol, hexamethylene glycol, pentaerythritol, methyl trimethylol methane, erythritol, 1 - 4 - di-(b -hydroxyethyl) benzene, decamethylene glycol, diethylene glycol, sorbitol, cyclohexyl 1-2-dicarbinol or the like. The monofunctional acids include the acids of linseed, soya, coconut, perilla, oiticica, corn and cottonseed oils, lauric, p-toluic, quinolinic, oleic, stearic and phenoxy acetic acids. Suitable a -g -diolefinic acids are hexadien-2-4-oic, 2-methyl hexadien-2-4-oic, 4-ethyloctadien-2-4-oic, 5-9-dimethyldecatrien-2-4-8-oic, octatrien - 2 - 4 - 8 - oic, 7 - phenylhaptatrien - 2-4-6-oic, D -1-3-cyclopentadien carboxylic, 5-cyclohexylpentadien-2-4-oic, 3-(D -1-3-cyclohexadienyl) propenoic, octatrien-2-4-6-carboxylic, 2-phenylhexadien-2-4-oic, 4-methylheptadien-2-4-oic, 5-9-dimethyl decatrien-2-4-8-oic, b -ionylidene acetic, 3-5-dimethyl hexadien-2-4-oic, 2-furyl hexadien-2-4-oic, 5-(2-furyl) pentadien-2-4-oic, cinnamalacetic, a -methyl cinnamalacetic, a -cyano-cinnamal-acetic, 2-5-diphenyl pentadien-2-4-oic, 2-furyl-5-phenyl pentadien-2-4-oic, 7-phenyl heptatrien-2-4-6 carboxylic acid-4, 5-methyl-5-phenyl pentadien-2-4-oic, 5-5-diphenyl pentadien-2-4-oic, p-tolyl pentadien-2-4-oic, 2-cyclohexyl-5-phenyl-pentadien-2-4-oic, 2-cyclopentadienyl-5-phenyl-pentadien-2-4-oic, 2-cyano-hexadien-2-4-oic, 2-cyano-5-9-dimethyl decatriene-2-4-8-oic, 2-cyano-3-6-dimethyl hexadien-2-4-oic, 2-4-dicyano-hexadien-2-4-oic, 2-methyl-4-cyano-hexadien-2-4-oic, 2-cyano-5-phenyl pentadien-2-4-oic, 2-cyano-octadien-2-4-oic, 2-cyano-4-methyl-7-phenyl-heptatriene-2-4-6-oic, 4-cyano-hexadien-2-4-oic, 2-cyano-5-cyclohexyl pentadien-2-4-oic, a -cyano-a -(b -ionylidene) acetic, b -(2-furyl) acrylic, a -methyl-b -(2-furyl) acrylic, a -cyano-b -(2-furyl) acrylic, a -b -di-(2-furyl) acrylic, a -phenyl-b -(2-furyl) acrylic, a -b -dimethyl-b -(2-furyl) acrylic, b -cyclohexyl-b -(2-furyl) acrylic, b -(3-furyl) acrylic, b -[2-(5-methylfuryl)] acrylic, and b -[2-(5-chlorofuryl)] acrylic acids, which are referred to as super-drying acids. In carrying out the esterifications, oxygen or substances yielding it should be excluded and consequently solvents such as aged turpentine or aged petroleum naphtha should not be used. A number of suitable solvents are listed. In the examples: (2) linseed oil is heated with glycerol and the product is then heated with hexadien-2-4-oic acid; (5) penta-erythritol is esterified with coconut oil acids and hexadien-2-4-oic acid; (6) an ester similar to that of example (2) is heated with linseed oil to form a modified ester; (10) linseed oil is heated with glycerol and the product is heated with b -(2-furyl) acrylic acid; (17) the penta-erythritol tri-ester of linseed oil acids is heated with glycerol di-ester of linseed oil acids and b -(2-furyl) acrylic acid; (18) a -methyl-b -(2-furyl) acrylic acid is esterified with glycerol di-ester of linseed oil acids; (19) glycerol dibenzoate is esterified with b -(2-furyl) acrylic acid; (25) linseed oil is heated with glycerol and the product is esterified with 2-cyano-hexadien-2-4-oic acid; (27) glycerol mono-ester of soya bean oil acids is esterified with 2-cyano-hexadien-2-4-oic acid; (28) and (29) di- and mono-glycerol esters of linseed oil acids are esterified with cinnamal acetic acid; (34) hexamethylene glycol, linseed oil acids and a -cyano-cinnamal-acetic acid are esterified together. Paints and varnishes.-The product of example (2), bodied by heating under nitrogen, is heated with a phenolic-modified ester gum; hydrated lime, litharge, the unbodied oil, and manganese resinate are added, and the mixture is again heated, and finally thinned with a hydrocarbon; a white and a black enamel are prepared from the same oil. The product of example (5) is mixed with a butyl acetate solution of nitrocellulose to form a lacquer. The product of example (10) is made into a black and a white enamel. The product of example (18) is made into a varnish by a method similar to that employed with the product of example (2). In examples (22) and (23) describe, the production of a varnish and an enamel from the product of example (10) in a similar manner. The product of example (25) is made into a varnish and an enamel similarly. The product of example (28) is made into an enamel base and a varnish, and the product of example (29) into an enamel. a -g -Diolefinic acids.-4-Ethyl-octadien-2-4-oic, octatrien-2-4-6-oic, 7-phenyl-heptatrien-2-4-6-oic, 5-cyclohexyl-pentadien-2-4-oic, 4-methyl-heptadien-2-4-oic, 5-9-dimethyl-decatrien-2-4-8-oic, 5-(2-furyl)-pentadien-2-4-oic, 5-5-diphenyl-pentadien-2-4-oic, 5-(p-tolyl)-pentadien-2-4-oic, and 4-cyano-hexadien 2-4-oic acids are made by condensing malonic ester with 2 - ethyl - hexanol, CH3.CH=CH-CH= CH.CHO, PhCH=CH-CH=CH-CHO, C6H11CH=CH-CHO, C2H5-CH=CMe.CHO, citral b - (2 - furyl) acrolein, Ph2C=CH.CHO, p-methyl cinnamic aldehyde, and a -cyano-crotonaldehyde respectively. 5-9-Dimethyl decatrien-2-4-8-oic acid is made by condensing citral with methyl acetate. D -1-3-Cyclopentadien carboxylic acid is made from cyclopentadiene, carbon dioxide and potassium. 3-(D -1-3-cyclohexadienyl) propenoic acid is made by condensing D -1-3-cyclohexadienal with malonic acid. Octatrien-2-4-6-carboxylic acid-4 is made by condensing crotonaldehyde with CH3-CH=CH-CHBr-COOEt in presence of zinc. 2-Phenyl-hexadien-2-4-oic acid is made by condensing crotonaldehyde with a -bromophenylacetic ester in presence of zinc. b -Ionylidene acetic acid is made by condensing b -ionone with bromacetic ester. 3-5-Dimethyl-hexadien-2-4-oic acid is made by condensing mesityloxide with bromoacetic ester in presence of zinc. 2-Furyl-hexadien-2-4-oic acid is made by condensing crotonaldehyde with a -bromo-(2-furylacetic) ester in presence of zinc. 2-5-Diphenylpentadien-2-4-oic acid is made by condensing cinnamic aldehyde with phenylacetic ester. 2-Furyl-5-phenyl-pentadien-2-4-oic acid is made by condensing cinnamic aldehyde with 2-furyl acetic ester. 7-Phenyl-heptatrien-2-4-6 carboxylic acid-4 is made by condensing cinnamic aldehyde with CH3-CH=CH-CH=CH-COOEt. 3-Methyl-5-phenyl-pentadien-2-4-oic acid is made by condensing benzalacetone with bromacetic ester. 2-Cyclohexyl-5-phenyl-pentadien-2-4-oic acid is made by condensing cinnamic aldehyde with cyclohexyl acetic ester. 2-Cyclopentadienyl-5-phenyl-pentadien-2-4-oic acid is made by the action of potassium on cinnamic aldehyde chloracetic acid, and cyclopentadiene. 2-Cyano-5-9-dimethyl-decatrien-2-4-8-oic and p 2-cyano-3-6-dimethyl-hexadien-2-4-oic acids are made by condensing citral and mesityl oxide respectively with cyanoacetic ester. 2-4-Dicyano-hexadien-2-4-oic and 2-methyl-4-cyano-hexadien-2-4-oic acids are made by reacting sodium cyanide with 2-cyano-4-chlorhexadien-2-4-oic and 2-methyl-4-chlorohexadien-2-4-oic acid respectively. 2-Cyano-5-phenyl-pentadien-2-4-oic, 2-cyano-octadien-2-4-oic and 2-cyano-4-methyl 7-phenyl-heptatrien-2-4-6-oic acids are made by condensing cyanoacetic ester with a -methyl cinnamic aldehyde, hexen-2-al-1, and Ph-CH=CH-CH=CMe-CHO respectively. 2-Cyano-5-cyclohexyl-pentadien-2-4-oic acid is made by condensing b -cyclohexyl acrolein with cyanoacetic ester. a -Cyano-a -(b -ionylidene) acetic acid is made by condensing b -ionone with bromoacetic ester. a -Methyl-b -(2-furyl) acrylic acid is made by reacting furfural with methyl propionate and sodium. a -b -di-(2-furyl) acrylic and a -phenyl-b -(2-furyl) acrylic acids are made by reacting furfural with 2-furylacetic ester and sodium and with phenylacetic acid re respectively. a -b -Dimethyl-b -(2-furyl) acrylic acid is made by reacting methyl furyl ketone with methyl-a -bromo-propionate and dehydration. b -Cyclohexyl-b -(2-furyl) acrylic acid is made by reacting cyclohexyl furyl ketone with methyl bromoacetate and dehydration. b -(3-furyl) acrylic, b -[2-(5-methylfuryl)] acrylic, and b -[2-(5-chlorfuryl)] acrylic acids are made by reacting 3-aldehydofuran, 5-methylfurfural, and 5-chlorfurfural respectively with acetic anhydride and sodium acetate.