The invention relates to the novel dihydrothienopyrimidine sulfoxides of formula (I) and to the pharmacologically acceptable salts thereof, wherein X represents SO or SO2, preferably however SO, and wherein R3, R4, R4′, R5, R6 and R7 are defined as in claim 1. The invention also relates to pharmaceutical compositions containing said compounds. The novel dihydrothienopyrimidine sulfoxides are suitable for use in the treatment of respiratory or gastrointestinal disorders or diseases, inflammatory diseases of the joints, the skin or the eyes, diseases of the peripheral or central nervous system or cancers.