Hyperidentities have been studied both in general and for specific varieties of algebras. In the latter case, attention has focussed on varieties of type (2), varieties of semigroups, and recently on inverse semigroup varieties of type $(2,1)$. In this paper we investigate hyperidentities for another family of type $(2,1)$ varieties, the varieties of star-bands. Using Petrich's equational description of the lattice of all star-band varieties, we present separating hyperidentities satisfied by these varieties.