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, 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.