The present invention relates to a process for the preparation of methacrylic acid or methacrylic esters, comprising the process steps of IA) preparation of 3-hydroxyisobutyric acid by a process comprising the process step of bringing a cell which has been genetically modified in comparison with its wild type in such a way that it is capable of forming more 3-hydroxyisobutyric acid, or polyhydroxyalkanoates based on 3-hydroxyisobutyric acid in comparison with its wild type, into contact with a nutrient medium comprising, as carbon source, carbohydrates, glycerol, carbon dioxide, methanol, L-valine or L-glutamate under conditions under which 3-hydroxyisobutyric acid or polyhydroxyalkanoates based on 3-hydroxyisobutyric acid are formed from the carbon source, if appropriate, isolation of the 3-hydroxyisobutyric acid from the nutrient medium and also, if appropriate, neutralization of the 3-hydroxyisobutyric acid, IB) dehydration of the 3-hydroxyisobutyric acid with formation of methacrylic acid and also, where appropriate, esterification methacrylic acid. The invention also relates to a process for the preparation of polymethacrylic acid or polymethacrylic esters.