Dihydrothienopyrimidinesulphoxides of formula 1 wherein X is SO or SO2, R1 is H or C1-6-alkyl, R2 is H or an organic group as disclosed herein, and R3 is an optionally substituted, mono- or bicyclic, unsaturated, partially saturated or saturated heterocycle or an optionally substituted, mono- or bicyclic heteroaryl, and the pharmacologically acceptable salts thereof, as well as pharmaceutical compositions which contain these compounds. These dihydrothienopyrimidinesulphoxides are suitable for the treatment of respiratory or gastrointestinal complaints or diseases, inflammatory diseases of the joints, skin or eyes, diseases of the peripheral or central nervous system, or cancers.