The invention relates to phenyl-1,2,4-oxadiazolone derivatives with phenyl group and to their physiologically acceptable salts and physiologically functional derivatives showing PPARdelta agonist activity. What are described are compounds of the formula I, ##STR00001## 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 and demyelinating and other neurodegenerative disorders of the central and peripheral nervous system.