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The practical realization of energy-efficient computing vectors is imperative to address the break-down in the scaling of power consumption with transistor dimensions, which has led to substantial underutilized chip space. Memristive elements that encode information in multiple internal states and reflect the dynamical evolution of these states are a promising alternative. Herein we report the observation of pinched loop hysteretic type-II memristive behavior in single-crystalline nanowires of a versatile class of layered vanadium oxide bronzes with the composition δ-[M(H2O)4]0.25V2O5 (M = Co, Ni, Zn), the origin of which is thought to be the diffusion of protons in the interlayer regions.