Simultaneous measurements of the longitudinal (sx) and transverse (sz) components of the turbulent fluctuating velocity gradient at the wall of a pipe are presented for ten locations in the transverse direction. Separate measurements of sx and of sz are also presented for twenty locations. The sz pattern reveals alternating positive and negative values over lengths Λ of the magnitude suggested by the spacing of the streaky wall structure observed in a number of laboratories. Of particular interest is the observation of regular eddies for which the sz pattern is accompanied by a spatial variation of sx out of phase by about 1/4Λ. These regular eddies are associated with intermittent production of Reynolds stress and with the occurrence of large negative values of sx which could be identified with wall bursts previously reported. The time response of the axial flow appears to influence the development of these regular eddies in that the development of an sx pattern lags behind that of an sz pattern. Measurements of spatial correlations of sx and sz with different time delays, as well as direct observations of the temporal variation of sx and sz patterns, support these notions.