In the last half century,there were several attempts to adopt the notion of supervenience in order to shed light on the claim of generality that is involved in aesthetic judgments. In this paper I will show the difficulties brought up by the transposition of the notion of supervenience from other areas of philosophy to the philosophy of art and I will also show the intrinsic difficulties of this project. First, I will revise the origins of the notion of supervenience in (...) contemporary ethics and philosophy of mind, as well as the theoretical framework in which this notion was first introduced. Second, I will revise the arguments for and against aesthetic supervenience in the field of analytic philosophy of art. In the rest of this work, I will try to argue against the viability of applying this notion to the relationship between aesthetic and non-aesthetic properties. I will point out the difficulties of identifying the base properties of such relationship, and then the difficulties of identifying the supervenient properties. In this way I will show that there are good reasons to argue that it will not be fruitful to use the notion of supervenience in order to understand the peculiarities of aesthetic judgments. Finally, I will point out a number of additional difficulties for the thesis of aesthetic supervenience which do not seem able to be satisfactorily solved. (shrink)