Effects of the Cu-site substitution on the 1/8 anomaly in the Bi-2212 and Y-123 phases and also on the anomaly at x = 0.21 in La sub(2-x)Sr sub(x)CuO sub(4) (LSCO) have been investigated from the transport, muon-spin relaxation and neutron-scattering measurements. It is suggested that the dynamical stripe correlations of spins and holes exist in the Bi-2212 and Y-123 phases as well as in the La-214 phase and that they tend to be pinned by Zn at the hole concentration of similar to1/8 per Cu in the high-T sub(c) cuprates and also at x = 0.21 in LSCO. Based upon the stripe-pinning model, universal properties in the high-T sub(c) cuprates that partially substituted Zn is a strong scatterer and that the Zn substitution markedly suppresses the superconductivity are also discussed. copyright 2001 Elsevier Science B.V. All rights reserved.