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Several conceptions of trope bundles have postulated mutual relations of ontological dependence to explain the unity of the bundle. The idea is that a bundle is a plurality of tropes such that each one of them is dependent on any other. A variant of this idea is that there is a ‘nucleus’ of tropes all of them mutually dependent, and there is also a ‘periphery’ or ‘halo’ of tropes that are dependent on the tropes of the nucleus, but the tropes of the nucleus are not dependent on them. There are several theoretical advantages that trope bundles conceived in this way have. A weakness of the position nevertheless is that it requires an equivalence relation of dependence. But it has been normally supposed that dependence is a strict order, i.e. it is relation irreflexive, asymmetric and transitive. Several recent works have put into question this traditional assumption. Those recent criticisms are discussed and it is argued that they are not convincing. Further arguments are presented for the irreflexivity and transitivity of dependence, from which asymmetry follows. Dependence, then, appears to be in fact a strict order. This implies that most forms of nuclear trope bundles are unintelligible. But not all of them, because nuclear tropes with a unique nuclear trope are coherent.