A compound or its salt having the following formula (II) is used as an activator for PPAR .delta.: ##STR00001## in which each of R.sup.11 and R.sup.13 is a hydrogen atom, an alkyl group having 1 to 8 carbon atoms, an alkoxy group having 1 to 8 carbon atoms, an alkyl group having 1 to 8 carbon atoms and a halogen atom substituent, etc.; R.sup.12 is a hydrogen atom, an alkyl group having 1 to 8 carbon atoms, an alkoxy group having 1 to 8 carbon atoms, an alkyl group having 1 to 8 carbon atoms and a halogen atom substituent, etc.; each of R.sup.14 and R.sup.15 is a hydrogen atom, an alkyl group having 1 to 8 carbon atoms, or an alkyl group having 1 to 8 carbon atoms and a halogen atom substituent; X.sup.1 is CH or N; Z.sup.1 is an oxygen atom or a sulfur atom; W.sup.1 is an oxygen atom or CH.sub.2; and q is an integer of 2 to 4.