The correlation between Fourier velocity components at the same wave numberkand two instants separated by a time &tgr; is investigated for a homogeneous, isotropic, and stationary turbulent field. Ensemble averages of four velocity components are related to second‐order averages as in a normal distribution. A power series in &tgr; for the time‐displaced kinetic energy spectrumE(k, &tgr;) is derived and the coefficient of &tgr;2evaluated explicitly using the Heisenberg spectrum for &tgr; = 0. The asymptotic behavior of this term for an infinite Reynolds numberRshows that the relaxation time associated with eddies of wave numberkvaries ask−1. These results were verified by numerical integrations for finite largeR. The resulting discrepancy with the dimensional result &tgr;k&agr;k−2/3is ascribed to the nonuniversality of the method of analysis followed. A general integrodifferential equation forE(k, &tgr;) is then derived and shown to admit solutions in similarity variables of the form &xgr; =k&tgr;1/&bgr;. The case &bgr; = 2/3 corresponds to the Kolmogoroff spectral law. Recent objections to the quasi‐normal approximation are criticized briefly in an appendix.