The present invention relates in general terms to a process for preparing alkyl methacrylates, comprising as steps: providing an acetone cyanohydrin by a process according to one of the preceding claims; contacting the acetone cyanohydrin with an inorganic acid to obtain a methacrylamide; contacting the methacrylamide with an alcohol in the presence of an inorganic acid in a reactor to obtain an alkyl methacrylate; continuously discharging at least a portion of the alkyl methacrylate from the reactor into a distillation column as a vapor stream; the discharge being effected by feeding a discharge stream comprising steam into the reactor, to an apparatus for preparing alkyl methacrylates, to a process for preparing polymers based at least partly on alkyl methacrylates, to the use of the alkyl methacrylates obtainable by the process according to the invention in chemical products, and to chemical products based on alkyl methacrylates obtainable by the process according to the invention.