Zero field Cu NMR of the first and fourth nearest neighbours of Mn in spin glass CuMn (concentrations from 0.4% to 4.7%) have been detected for T<Tg/5. The enhancement factor &eegr; of the rf field and NMR signal intensity, associated with the rotation of domain magnetization, has been found roughly proportional to the remanent magnetization &sgr; and is negligible when the sample has been zero field cooled. These results contradict the independent domain model for which &eegr; should be independent of &sgr;. The data reveal the existence of a well defined anisotropy field HAinduced (as &sgr;) by the cooling field Hc, the anisotropy energy being roughly a constant. Transverse susceptibility and NMR intensity analyses confirm that most Mn spins are involved in the collective response to a transverse field and that HAis defined on a macroscopic scale. Direct observation by NMR of the shifted hysteresis loops and comparison with magnetization data imply that HAincludes both an uniaxial Hax) and an unidirectional (Hd) anisotropy field, and that the magnetization reversals, when detected, occur for fields ‖Ho+Hd‖<Hax. The simultaneous occurrence of collective and irreversible phenomena in spin glasses is discussed.