Jaegwon Kim and others have claimed that (strong) psychophysical super
venience entails the reducibility of mental properties to physical pro
perties. I argue that this claim is unwarranted with respect to episte
mic (explanatory) reducibility (either of a 'global' or of a 'local' s
ort), as well as with respect to ontological reducibility. I then atte
mpt to show that a robust version of nonreductive materialism (which I
call 'supervenient token-physicalism') can be defended against the ch
arge that nonreductive materialism leads to epiphenomenalism in failin
g to account for the causal or explanatory relevance of mental propert
ies.