The invention relates to oxadiazolones and to their physiologically acceptable salts and physiologically functional derivatives showing PPAR delta agonist activity. What is described are compounds of the formula (I) in which the radicals are as defined, and their physiologically acceptable salts and processes for their preparations. The compounds are suitable for the treatment and/or prevention of disorders of fatty acid metabolism and glucose utilization disorders as well as of disorders in which insulin resistance is involved; neurodegenerative diseases and/or demyelinating disorders of the central and peripheral nervous systems and/or neurological diseases involving neuroinflammatory processes and/or other peripheral neuropathies.