Local dynamics of polyacetylenes having polymethylated indan/tetrahydronaphthalene moieties have been studied using quasielastic neutron scattering, and the results obtained have been discussed together with former results with various poly(diphenylacetylene) derivatives. Clear quasielastic scattering was observed for the present polymers although they were in the glassy state, and the observed dynamic scattering laws were well fitted to a model function assuming the sum of narrow and broad Lorentzians. Both the relaxation rates and fractions from the narrow component exhibited a positive correlation with oxygen permeability coefficients (P-O2), while those from the broad component hardly related to P-O2. Furthermore, the local flux, which is defined as the product of fraction and relaxation rate of the narrow component, is also found to be proportional to P-O2. These findings imply that only the narrow component contributed to the gas permeability. Thus, it has been clarified that the local dynamics with a time scale of several tens of picoseconds plays a role of key importance for the gas permeability of substituted polyacetylenes in the glassy state. (C) 2013 Elsevier Ltd. All rights reserved.