The invention relates to oxadiazolones and to their physiologically acceptable salts and physiologically functional derivatives showing peroxisome proliferator activator receptor (PPAR) delta agonist activity comprising compounds of formula I, ##STR00001## in which the R1-R7 substituents as well as the U, V, W, X Y and z radicals are as defined herein, and their physiologically acceptable salts and processes for their preparation. 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 neuro-inflammatory processes and/or other peripheral neuropathies.