This paper is concerned with the notions of supervenience and mechanistic constitution as they have been discussed in the philosophy of neuroscience. Since both notions essentially involve specific dependence and determination relations among properties and sets of properties, the question arises whether the notions are systematically connected and how they connect to science. In a first step, some definitions of supervenience and mechanistic constitution are presented and tested for logical independence. Afterwards, certain assumptions fundamental to neuroscientific inquiry are made explicit (...) in order to show that the presented definitions of supervenience are virtually uninteresting for theory construction in this field. In a third step, a new formulation of supervenience is developed that makes explicit reference to the notion of constitution and that bridges the gap between the philosophical concepts and explanatory practice in neuroscience. (shrink)