Polymeric anhydrides, believed to be of the structure <PICT:0731053/IV (a)/1> where n has a value of the order of 10 are produced, together with cyclohexa-1,4-diene-1,4-dicarboxylic acid when a lactone such as 4-carbomethoxy - 2 - hydroxy - 6 - oxa - bicyclo-(3 : 2 : 1)-octa-7-one, of the structure <PICT:0731053/IV (a)/2> (formed by heating a cyclohexane-2,5-diol 1,4-dicarboxylic acid or esters thereof at at least 170 DEG C. in e.g. xylenols, decahydronaphthalene, diphenyl oxide or nitrobenzene) is heated further with the addition of an acid such as p-toluene sulphonic acid to the reaction mixture. The anhydride is also formed when cyclohexane-2,5 diol-1,4-dicarboxylic acid or mono- or diesters are heated with a chemical dehydrating agent, e.g. potassium hydrogen sulphate, phosphoric acid, sulphuric acid or a sulphonic acid, if desired in the presence of a high-boiling solvent. The anhydride is produced as an intermediate in several examples relating to the production of terephthalic acid and its mono- and diesters (see Group IV (b)).ALSO:A process for the production of terephthalic acid or acid esters or di-esters thereof comprises dehydrating cyclohexane - 2,5 - diol - 1,4 - dicarboxylic acid or acid esters or di-esters of, and simultaneously or subsequently dehydrogenating the cyclohexa-1,4-diene-1,4-dicarboxylic acids or acid esters or di-esters produced. The dehydration can be effected in four ways: (A) The cyclohexane-2,5-diol-1,4-dicarboxylic acid, acid ester or diester is heated at 200 DEG to 500 DEG C., e.g. in contact with inert granular material such as quartz chips, the dimethyl ester in the liquid or vapour phase, giving mainly methyl hydrogen cyclohexa-1,4-diene-1,4-dicarboxylate with minor amounts of the dimethyl ester and free acid. (B) The diol is heated at a temperature of at least 170 DEG C. in a solvent such as xylenols, decahydronaphthalene, diphenyl oxide or nitrobenzene. A lactone 4 - carbomethoxy - 2 - hydroxy - 6 - oxa - bicyclo-(3 : 2 : 1)-octa-7-one or the corresponding free acid (depending on the starting material) is formed, which on heating with acid gives cyclohexa-1,4-diene-1,4-dicarboxylic acid and a polymeric anhydride believed to have the formula <FORM:0731053/IV (b)/1> where n has a value of the order of 10. This polymer can be hydrolysed with aqueous caustic alkali to give the acid, which can then be re-esterified. (C) The diol may be contacted with a dehydration catalyst such as alumina, an alumina-silica gel, an activated clay, zinc oxide or basic aluminium phosphate at 200 DEG to 500 DEG C., the diester in the liquid or vapour phase, the acid ester or dicarboxylic acid in the liquid phase. (D) The diol is heated with a chemical dehydration catalyst such as potassium hydrogen sulphate, phosphoric acid, sulphuric acid or a sulphonic acid, product comprising the cyclohexa - 1,4 - diene - 1,4 - dicarboxylic acid and the polymeric anhydride (which may be converted with alkali to the acid which is then esterified). A solvent such as the xylenols, decahydronaphthalene or nitrobenzene may be present. The dehydrogenation of the cyclohexa - 1,4 - diene - 1,4 - dicarboxylic acid to terephthalic acid may be carried out in three ways: (a) The diene is subjected to thermal treatment at 150 DEG to 750 DEG C. By this means the whole process is effected thermally, e.g. with dehydration at 250 DEG to 350 DEG C. in the presence of toluene, followed by dehydrogenation at 450 DEG to 550 DEG C., or in a single stage at 350 DEG to 450 DEG C. (b) The diene is dehydrogenated in the vapour or liquid phase at 200 DEG to 650 DEG C. in the presence of a dehydrogenation catalyst such as a metal of Group VIII of the Periodic System or copper, in the finely-divided state or on a porous support, or the oxides of chromium, molybdenum or vanadium, mixed with or supported on other oxides. (c) The diene is oxidized to terephthalic acid by heating with sulphur or selenium conveniently at 150 DEG to 300 DEG C. In examples, cyclohexane-2,5-diol-1,4-dicarboxylic acid dimethyl ester is (1) passed continually in solution in toluene over quartz chips at 300 DEG C.; (2) heated in diphenyl oxide at 200 DEG C. in diphenyl oxide, to give 4-carbomethoxy-6-hydroxy - 6 - oxa - bicyclo (3 : 2 : 1) - octan - 7 - one. Heating this with p-toluene sulphonic acid gives cyclohexa-1,4-diene-1,4-dicarboxylic acid and its polymeric anhydride, which is converted to the acid by heating with aqueous sodium hydroxide; (3) dehydrated by heating at 150 DEG to 180 DEG C. with sulphuric acid; (4) dehydrated by passing it over basic aluminium phosphate at 350 DEG C. In examples: (6) to (8) cyclohexa - 1,4 - diene - 1,4 - dicarboxylic acid dimethyl ester is dehydrogenated to terephthalic acid or its esters by (6) passing it over a palladium on charcoal catalyst at 350 DEG C.; (7) heating at 290 DEG to 300 DEG C. with selenium; (8) passage over quartz chips at 400 DEG C. Cyclohexane - 2,5 - diol - 1,4 - dicarboxylic acid dimethyl ester is converted directly to dimethyl terephthalate, monomethyl terephthalate and terephthalic acid by (5) heating at 500 DEG C.; (9) passage over platinum on charcoal at 350 DEG C.; (10) passage over palladium on charcoal at 290 DEG to 310 DEG C. In examples 4, 8, 9 and 10 the reaction products are converted to the dimethyl ester by reaction with diazomethane. The cyclohexane - 1,4 - diol - 1,4 - dicarboxylic acid or esters thereof may be produced by treating a dialkyl succinate with a condensing agent such as an alkali or alkaline earth metal or an alkoxide thereof to produce the disodium derivative of a dialkyl cyclohexa-1,4-diene-2,5-diol-1,4-dicarboxylate, e.g. a compound of the di-sodio derivative of dimethyl cyclohexa-1,4-diene - 2,5 - diol - 1,4 - dicarboxylate (with two molecules of methanol) is produced by condensing dimethyl succinate in the presence of sodium methoxide. Such sodium salts can be converted to dialkyl cyclohexane-2,5-diol-1,4-dicarboxylates by hydrolysis to give, e.g. dimethyl cyclohexa - 1,4 - diene - 2,5 - diol - 1,4 - dicarboxylate which can then be hydrogenated, e.g. over a copper catalyst or Group VIII metal.