Process for preparing methyl methacrylate and/or methacrylic acid, comprising the process steps of: a. the reacting of acetone cyanohydrin and sulfuric acid in one or more reactors I in a first reaction stage at a temperature in the range from 70°C to 130°C to obtain a first reaction mixture comprising sulfoxyisobutyramide and methacrylamide; b. the converting of the first reaction mixture, comprising heating to a temperature in the range from 130 to 200°C, in one or more reactors II in a second reaction stage to obtain a second reaction mixture comprising predominantly methacrylamide and sulfuric acid; and c. the reacting of the second reaction mixture with water and optionally methanol in one or more reactors III in a third reaction stage to obtain a third reaction mixture comprising methacrylic acid and/or methyl methacrylate; wherein (i) the sulfuric acid used in the first reaction stage, which is fed in at one or more points in the reactors I, has a concentration in the range from 98.0% by weight to 100.5% by weight, (ii) the dwell time of the first reaction mixture in the second reaction stage is in the range from 2 to 15 min, (iii)the heating in the second reaction stage is performed in one or more reactors II, wherein at least one reactor II comprises at least one preheater segment comprising one or more linear pipeline elements that are heated by means of a heating medium spatially separate from the reaction mixture, wherein the reaction mixture is heated by 10 to 100°C, (iv) the converting in the second reaction stage is performed in one or more reactors II, wherein at least one reactor II comprises at least one delay segment which is operated under virtually adiabatic conditions, (v) the preheater segment and/or the delay segment are implemented in a combination of linear pipeline elements and deflections, wherein the linear pipeline elements and the deflections are connected to one another via reducing flanges, (vi) the second reaction mixture obtained in step b, comprising predominantly methacrylamide and sulfuric acid, is optionally cooled down to a temperature below 120°C, and/or optionally intermediately buffered in an intermediate vessel, before the reaction mixture is guided into the third reaction stage, wherein the superficial volume of the linear pipeline elements relative to the superficial volume of the deflections in at least one preheater segment corresponds to a ratio in the range from 2.0 to 75.0. a. the reacting of acetone cyanohydrin and sulfuric acid in one or more reactors I in a first reaction stage at a temperature in the range from 70°C to 130°C to obtain a first reaction mixture comprising sulfoxyisobutyramide and methacrylamide; b. the converting of the first reaction mixture, comprising heating to a temperature in the range from 130 to 200°C, in one or more reactors II in a second reaction stage to obtain a second reaction mixture comprising predominantly methacrylamide and sulfuric acid; and c. the reacting of the second reaction mixture with water and optionally methanol in one or more reactors III in a third reaction stage to obtain a third reaction mixture comprising methacrylic acid and/or methyl methacrylate; (i) the sulfuric acid used in the first reaction stage, which is fed in at one or more points in the reactors I, has a concentration in the range from 98.0% by weight to 100.5% by weight, (ii) the dwell time of the first reaction mixture in the second reaction stage is in the range from 2 to 15 min, (iii)the heating in the second reaction stage is performed in one or more reactors II, wherein at least one reactor II comprises at least one preheater segment comprising one or more linear pipeline elements that are heated by means of a heating medium spatially separate from the reaction mixture, wherein the reaction mixture is heated by 10 to 100°C, (iv) the converting in the second reaction stage is performed in one or more reactors II, wherein at least one reactor II comprises at least one delay segment which is operated under virtually adiabatic conditions, (v) the preheater segment and/or the delay segment are implemented in a combination of linear pipeline elements and deflections, wherein the linear pipeline elements and the deflections are connected to one another via reducing flanges, (vi) the second reaction mixture obtained in step b, comprising predominantly methacrylamide and sulfuric acid, is optionally cooled down to a temperature below 120°C, and/or optionally intermediately buffered in an intermediate vessel, before the reaction mixture is guided into the third reaction stage,