The invention comprises di-lactams having the general formula <FORM:0824207/IV (b)/1> wherein R represents -CH2-, -CH2-CH2-CH3-CH<, (CH3)2CH-CH<, =CH-CH= CH-CH3, -CH2-O-CH2- or -CH2-O-CH2-CH2-, Z represents the grouping -NH-CO- or -CO-NH- and A represents -(CH2)n-, -(CH2)n1 -CH(CH3)-(CH2)n2-or -(CH2)n3-CH(CH3)-(CH2) n4-CH(CH3)-(CH2)n5-, n being a whole number from 1 to 6, n1 and n2 being whole numbers from 0 to 5 but (n1 + n2) not being more than 5 and n3, n4 and n5 being whole numbers from 0 to 4 but (n3 + n4 + n5) not being more than 4. They may be prepared by subjecting dioximes of the general formula <FORM:0824207/IV (b)/2> to the action of compounds known to be capable of effecting the Beckmann rearrangement of oximes, e.g. sulphuric acid, oleum, chlorsulphonic acid, perchloric acid, HF, PCl5, POCl3, antimony chloride, acetyl chloride, BF3 and benzene sulphonyl chloride. Temperatures above or below atmospheric, e.g. 60-220 DEG C., may be used. Solvents or diluents may be present and cooling may be effected by vaporization thereof. Continuous and batchwise procedures are described. The di-lactams, which generally occur as isomeric mixtures, may be recovered by neutralization, followed by extraction with a solvent and precipitation from the extract by addition of a non-solvent or followed by removal of the salts, e.g. by filtration and treatment with an ion-exchange agent and then evaporation of the filtrate. Further purification may be effected by re-dissolution and precipitation or by recrystallization, preferably after treatment with an adsorption agent. The dilactams may be converted into polyamides (see Group IV (a)). Examples describe the rearrangements of methylene - bis - cyclohexanone - oxime and 1:11 - di - (2 - ketocyclohexyl)dimethyl ether dioxime and numerous other suitable dioximes are named, including those derived from cycloalkanones ranging from cyclopropanone to cyclo-octanone. The dioximes may be prepared by the action of hydroxylamine on the corresponding diketones; the methylene bis-(cycloalkyl ketones) may be obtained by reacting the appropriate ketone with formaldehyde or its chemical equivalent.ALSO:Polyamides having a partly cross-linked structure are prepared by thermal condensation at 120-300 DEG C., while excluding oxygen, of dilactams having the general formula <FORM:0824207/IV (a)/1> wherein R represents -CH2-, -CH2-CH2-, CH3-CH=, =CH-CH(CH3)2, =CH-CH =CH-CH3, -CH2-O-CH2- or -CH2 -CO-CH2-CH2-, Z represents the grouping -NH-CO or -CO-NH- and A represents -(CH2)n-, -(CH2)n, -CH(CH3)-(CH2)n2-or -(CH2)n3-CH(CH3) -(CH2)n4-CH(CH3) (CH2)n5-, wherein n is a whole number from 1-6, n1 and n2 are whole numbers from 0 to 5, but (n1 + n2) not being greater than 5, and n3, n4 and n5 are whole numbers from 0 to 4 but (n3 + n4 + n5) not being greater than 4. The di-lactams may be condensed alone or with linear polyamides or compounds forming linear polyamides such as mixtures of aliphatic diamines and C4-C20 aliphatic dicarboxylic acids, and non-polymeric compounds which are obtained by reacting such diamines with dicarboxylic acids or contain in the molecule at least one lactam group or both at least one amino group and at least one carboxylic or carboalkoxy group. Examples are the adipic, sebacic or suberic acid salts of hexamethylene diamine, the adipic acid salts of octamethylene diamine and diamino dicyclohexyl methane, omegaamino caproic acid or its hydrochloride, omegaamino oenanthic acid, omega-amino undecanic acid, acetyl amino caproic acid, pyrrolidone, epsilon caprolactam, oenanthic lactam, caprylic lactam and mixtures of such compounds. The dilactams may constitute from 0.5 to 90% by weight of the final polyamide. Polycondensation may be effected under reduced as well as elevated pressures and in the presence of a solvent or diluent. Condensation promoters such as water, benzoic acid, epsilon amino caproic acid, and its hydrochloride, hexamethylene diamine adipate, alkali or alkaline earth metals, alkali hydroxides and alkali amides, stabilizers such as adipic acid, acetic acid and stannous chloride, and softeners such as hydroxy benzoic acid esters, benzene sulphonic acid monomethylamide, dibenzylphenol, resorcinol phosphate and isododecyl phenol may be present. A condensing-in may be effected by annealing at 120 DEG -300 DEG C. before or during the working up. Cross-linking of the linear polyamides by condensing in the di-lactams may be effected by mixing or kneading the polyamides with the dilactams at slightly below the M.P. of the polyamide; the polyamides may be compressed under, say, 3000-6000 atmospheres with the dilactams and condensing-in then affected by annealing at slightly below the M.P. of the polyamide. The condensations may also be effected in moulds. The final polymers may be shaped into fibres, films, sheets or tubes; the mixed polycondensates have improved adherence p to metal, glass, paper and rubber and have improved waterproofness. In typical examples: (7) epsilon caprolactam and methylene-bis-caprolactam are condensed together in water at 275 DEG C. in an autoclave in the absence of oxygen; (8) a mixture of the lactams of (7) containing a little adipic acid salt of hexamethylene diamine with or without some water is similarly polycondensed; (12) caprylic lactam mixed with small amounts of water and methylene-bis-caprolactam is polycondensed as in (7); (14) a mixture of epsilon-caprolactam, water and a minor amount of the dilactam obtained by Beckmann rearrangement of the dioxime of 1.11 - di - (2 - keto cyclohexyl) dimethyl ether is heated in absence of oxygen 270 DEG C. in an autoclave under 16 atmos. pressure and subsequently under pressures reducing to atmospheric; (15) methylene-bis-caprolactam, o-hydroxydiphenyl and some hexamethylene diamine adipate are heated as in (7) yielding a polyamide solution from which the solvent is removed with methanol; (16) the lactam of (14) is heated with caprolactam and hexamethylene diamine adipate in p-cresol as in (7) and thereafter the solvent is distilled from the resin in vacuo.