Process for preparing methacrylic acid and/or alkyl methacrylate, preferably methyl methacrylate, comprising: a. reacting acetone and hydrogen cyanide in the presence of a basic catalyst in a first reaction stage (synthesis of ACH) to obtain a first reaction mixture comprising acetone cyanohydrin; b. working up the first reaction mixture comprising acetone cyanohydrin; c. reacting acetone cyanohydrin and sulfuric acid in one or more reactors I in a second reaction stage (amidation) at an amidation temperature in the range from 85°C to 130°C to obtain a second reaction mixture comprising sulfoxyisobutyramide and methacrylamide; d. converting the second reaction mixture, comprising heating to a conversion temperature in the range from 130°C to 200°C, in one or more reactors II in a third reaction stage (conversion) to obtain a third reaction mixture comprising predominantly methacrylamide and sulfuric acid; e. reacting the third reaction mixture with water and optionally alcohol, preferably water and optionally methanol, in one or more reactors III in a fourth reaction stage (hydrolysis or esterification) to obtain a fourth reaction mixture comprising methacrylic acid and/or alkyl methacrylate, preferably methyl methacrylate; f. optionally separating alkyl methacrylate from the fourth reaction mixture obtained from the fourth reaction stage; wherein the sulfuric acid used in the second reaction stage has a concentration in the range from 98.0% by weight to 100.0% by weight; wherein a pure ACH mixture which is used in the second reaction stage has a water content within a range from 0.1 mol% to 10 mol%, especially 0.4 mol% to 5 mol%, based on ACH present in the pure ACH mixture, and wherein a total amount of water used in the second reaction stage is within a range from 0.1 mol% to 20 mol%, especially 0.4 mol% to 10 mol%, based on ACH present in the pure ACH mixture. a. reacting acetone and hydrogen cyanide in the presence of a basic catalyst in a first reaction stage (synthesis of ACH) to obtain a first reaction mixture comprising acetone cyanohydrin; b. working up the first reaction mixture comprising acetone cyanohydrin; c. reacting acetone cyanohydrin and sulfuric acid in one or more reactors I in a second reaction stage (amidation) at an amidation temperature in the range from 85°C to 130°C to obtain a second reaction mixture comprising sulfoxyisobutyramide and methacrylamide; d. converting the second reaction mixture, comprising heating to a conversion temperature in the range from 130°C to 200°C, in one or more reactors II in a third reaction stage (conversion) to obtain a third reaction mixture comprising predominantly methacrylamide and sulfuric acid; e. reacting the third reaction mixture with water and optionally alcohol, preferably water and optionally methanol, in one or more reactors III in a fourth reaction stage (hydrolysis or esterification) to obtain a fourth reaction mixture comprising methacrylic acid and/or alkyl methacrylate, preferably methyl methacrylate; f. optionally separating alkyl methacrylate from the fourth reaction mixture obtained from the fourth reaction stage; wherein the sulfuric acid used in the second reaction stage has a concentration in the range from 98.0% by weight to 100.0% by weight; wherein a pure ACH mixture which is used in the second reaction stage has a water content within a range from 0.1 mol% to 10 mol%, especially 0.4 mol% to 5 mol%, based on ACH present in the pure ACH mixture, and wherein a total amount of water used in the second reaction stage is within a range from 0.1 mol% to 20 mol%, especially 0.4 mol% to 10 mol%, based on ACH present in the pure ACH mixture.