Positive exponent superplasticity (exhibits superplastic behavior at very high strain rates over 1 s-1) has been observed in nano or near-nano scale aluminum alloys, which have been developed to be 50-500 nm in grain sizes by advanced processing methods. The experimental results on high-strain-rate superplastic materials are reviewed and related to the dependencies of the ability of superplasticity on grain size and the nature of grain boundaries, as well as the state of materials. The optimum superplastic strain rates are found to be strongly dependent on the refinement of grain structures, also the superplastic elongations were critically controlled by the accommodation process to relax the stress concentration resulting from grain boundary sliding, involving an accommodation helper such as soft phases, amorphous phases or liquid phases.