We report NMR measurements of the nuclear relaxation rate at all copper and oxygen sites in magnetically aligned powder samples of YB^CM^OI.Comparison of the oxygen and copper relaxation reveals a characteristic temperature greater than T c . The copper relaxation rate is enhanced by antiferromagnetic copper spin fluctuations which are undiminished in the superconducting state. The absence of a coherence peak indicates that the superconductive pairing is not of the conventional BCS type. PACS numbers: 74.70.Vy, 74.30.Gn, 76.60.Es, 76.60.Jx The nature of spin fluctuations in the hightemperature superconducting copper oxides and their possible role in superconductive pairing are problems of central importance in our understanding of these materials. Nuclear-magnetic-relaxation-rate (TT l ) measurements microscopically probe spin dynamics at the atomic sites and so provide crucial insight into this question. Accordingly we have measured the relaxation rate at all oxygen and copper sites in magnetically aligned powders l of YBa2Cu307. Comparison of the copper and oxygen NMR relaxation rates shows that the large magnitude of the copper relaxation rate in the normal state is due to antiferromagnetic copper spin fluctuations and that these antiferromagnetic spin fluctuations persist into the superconducting state. The behavior of these fluctuations changes 0.1 D 0.01 0.001 -I