ABSTRACT. We present a fuzzy (or quantitative) version of the van Benthem theorem, which characterizes propositional modal logic as the bisimulation-invariant fragment of first-order logic. Specifically, we consider a first-order fuzzy predicate logic logic along with its modal fragment, and show that the first-order formulas that are non-expansive w.r.t. the natural notion of bisimulation distance are exactly those that can be approximated by modal formulas.