The fully‐developed turbulent flow generated by a grid is axisymmetric, the intensity of the axial turbulence component being greater than that of the lateral component. Since the mean‐velocity distribution is uniform and consequently, the gradient of the mean velocity is zero everywhere, a local stress‐strain relationship is not possible. Measurements of the turbulence structure in a region up to 50 grid mesh‐sizes downstream of the grid, have revealed that long‐distance memory effects are responsible for a nonlocal relationship. In the local shear layers just downstream of the rods, the principal axes of the stress tensor make an angle of roughly 40 deg with the direction of the main flow. This angle decreases in the developing region, and becomes zero in the fully‐developed region. The plane of maximum shear stress then makes an angle of 45 deg with the direction of the main flow. The transport equations for turbulence are transformed to nonhomogeneous linear relaxation equations, which clearly show the long‐distance memory behavior of the maximum shear stress.