We have examined the magnetic properties of polycrystalline, superconducting YBa_2(Cu_0.96Ni_0.04)_3O_y (y ~ 7, T_sc ~ 75 K) using two local probe techniques: 170Yb Moessbauer down to 0.1 K and muon spin relaxation (muSR) down to 1.5 K. At 0.1 K, the 170Yb measurements show the Cu(2) over essentially all the sample volume carry magnetically correlated moments which are static on the time-scale of 10^{-9} s. The moments show a distribution in size. The correlations are probably short range. As the temperature increases, the correlated moments are observed to fluctuate with measurable rates (in the GHz range) which increase as the temperature increases and which show a wide distribution. The muSR measurements also evidence that the fluctuation rates increase with increasing temperature and there is a distribution. The evidenced fluctuating, correlated Cu(2) moments coexist at an atomic level with superconductivity.
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