Aminoalkylsulphonic acids, of the general formula <FORM:0406380/IV/1> , where R and R1 are hydrogen or any hydrocarbon radicle, or jointly, with the nitrogen atom, a heterocyclic nucleus, and R2 is an alkylene group, are manufactured by reacting mineral acid esters of hydroxyalkylamines, or salts thereof, with neutral alkali metal, alkaline earth metal or ammonium salts of sulphurous acid in the presence of some water. The quantity of water may be very small, traces thereof being sufficient, but usually the quantity should be at least equal to that of the mineral acid ester and preferably to that of both reaction components. Neutral or acid esters, or water soluble salts of the latter, from strong non-oxidizing mineral acids, e.g. sulphuric and phosphoric acids and halogen hydracids, are preferred, those from weak acids such as boric acid or from nitric acid being less suitable. Particularly suitable are the acid sulphuric esters of hydroxyalkylamines, obtainable for example by the process of Specification 377,695, or salts thereof, e.g. acid sulphuric esters of mono-, di- or triethanolamine, N-hydroxyethylaniline, N-ethyl-N-hydroxyethylaniline, N-hydroxyethyldiphenylamine (obtainable by heating diphenylamine in an autoclave with ethylene oxide), N-hydroxyethyl-N-benzylamine, N-hydroxyethylpiperidine, N-methyl-N - hydroxyethyl - N - octodecenylamine (obtainable by heating octodecenyl alcohol sulphuric ester with excess of methylamine in a closed vessel and heating the N-methyloctodecenylamine produced with ethylene oxide in an autoclave), N - hydroxyisopropyl - N - methyl - a -naphthylamine (obtainable by heating N-methyl - a - naphthylamine with a - propylene oxide), N - b - hydroxy - n - butyl - N - ethylaniline (obtainable by heating N-ethylaniline with 1 : 2-butylene oxide in a closed vessel), N-b -hydroxy-n-butyl-a - or b -naphthylamine (obtainable similarly from a - or b -naphthylamine), N - b - hydroxy - n - butyldiphenylamine (obtainable similarly from diphenylamine), N - g - hydroxy - n - butyl - N - benzyl - N - n - butylamine (obtainable by heating N-benzyl-N-n-butylamine with 1 : 3-butylene oxide in a closed vessel), N - g - hydroxypropylcyclohexylamine (obtainable by heating cyclohexylamine with 1 : 3-propylene oxide in a closed vessel), N-hydroxyethyl - N - benzylcyclohexylamine (obtainable by heating N-benzylcyclohexylamine with ethylene oxide in a closed vessel), N - butyl - N - b - hydroxypropylaniline (obtainable by heating N-butylaniline with 1 : 2-propylene oxide in a closed vessel) and similar N-aryl-N-hydroxyalkylamines of the general formula NRR1R2, where R is hydrogen or any alkyl, cycloalkyl, aryl or aralkyl radicle, R1 is an aryl or aralkyl radicle, e.g. phenyl, tolyl, xylyl, naphthyl or benzyl, and R2 is a hydroxyalkyl radicle. There may also be employed the corresponding halogen hydracid esters, e.g. butyl chlor-, brom- or iodoethylamine (obtainable by heating butylethanolamine in an autoclave with fuming hydrochloric, hydrobromic or hydriodic acid, in the last case in the presence of red phosphorus), or phosphoric esters or water-soluble salts thereof, especially the alkali metal salts. When employing acid mineral acid esters the reaction mixture is preferably neutralized by means of alkali. The reaction is generally carried out by warming in aqueous solution in a closed vessel, generally to about 120--180 DEG C., though in some cases the temperature should not exceed 160 DEG C. in order to avoid decomposition of the initial materials. Water-soluble, neutral and inert organic diluents, e.g. ethyl alcohol, glycol or acetone, may be added. Suitable sulphites are ammonium, sodium, potassium, lithium, calcium, barium, strontium and magnesium sulphites, especially the first three. The sulphites are advantageously employed in slight excess over the theoretical quantity. The products are intermediates for the preparation of assistants for the textile and related industries, dyestuffs and pharmaceutical preparations. In examples: (1) aminoethanol monosulphuric ester is heated with sodium sulphite in aqueous solution in an autoclave to produce taurine; (2) N - n - butyl - N - hydroxyethylaniline sulphuric ester (obtainable by heating N-n-butylaniline with ethylene oxide, mixing the product with concentrated sulphuric acid and pouring on to ice) is dissolved in water, neutralized with caustic soda and heated in an autoclave with sodium sulphite, yielding N-butyl-N-phenyltaurine sodium salt; (3) the sodium salt of N-methyl-N-hydroxyethylaniline sulphuric ester is heated in aqueous solution in a pressure-tight vessel with sodium sulphite, producing N-methyl-N-phenyltaurine sodium salt; (4) the sodium salt of N-hydroxyethyl-N-benzylaniline sulphuric ester (obtainable by heating N-benzylaniline in a closed vessel with ethylene oxide, treating the product with concentrated sulphuric acid and pouring on to ice) is heated in aqueous solution in a closed vessel with sodium sulphite, to yield N-benzyl-N-phenyltaurine sodium salt; (5) the acid sulphuric ester of N-ethyl-N-hydroxyethyl-a -naphthylamine (obtainable by heating N-ethyl-a -naphthylamine in an autoclave with ethylene oxide and treating the product with concentrated sulphuric acid) is dissolved in water, neutralized with caustic soda and heated in an autoclave with sodium sulphite to produce N-ethyl-N-a -naphthyltaurine, which is liberated by addition of sulphuric acid; (6) the sodium salt of the acid sulphuric ester of N-hydroxyethyldiphenylamine (obtainable by treating N-hydroxyethyldiphenylamine with concentrated sulphuric acid, pouring on to ice, neutralizing with caustic soda and evaporating to dryness) is heated in an autoclave in aqueous solution with sodium sulphite, yielding diphenyltaurine sodium salt.