The present invention is directed to 1,3,4-oxadiazalones, i.e., the compounds of formula I and their pharmaceutically acceptable salts, stereoisomers, tautomers, or solvates thereof. Novel compounds include those of formula I, in which radicals are as defined herein. ##STR00001## The compounds of this invention are modulators of PPARdelta and therefore useful as pharmaceutical agents, especially for the treatment of demyelinating diseases and disorders of fatty acid metabolism and glucose utilization such as multiple scleroses.