We have examined the magnetic properties of superconducting YBa2(Cu0.96Co0.04)3Oy (y ∼7, Tsc=65 K ) using elastic neutron scattering and muon spin relaxation (µSR) on single crystal samples. The elastic neutron scattering measurements evidence magnetic reflections which correspond to a commensurate antiferromagnetic Cu(2) magnetic structure with an associated Néel temperature TN ∼400 K. This magnetically correlated state is not evidenced by the µSR measurements. We suggest this apparent anomaly arises because the magnetically correlated state is dynamic in nature. It fluctuates with rates that are low enough for it to appear static on the time scale of the elastic neutron scattering measurements, whereas on the time scale of the µSR measurements, at least down to ∼50 K, it fluctuates too fast to be detected. The different results confirm the conclusions reached from work on equivalent polycrystalline compounds: the evidenced fluctuating, correlated Cu(2) moments coexist at an atomic level with superconductivity.