We have studied the magnetization in the spin‐glass phase ofAgMn under the repetitive application of a small (10 Oe≤h≤50 Oe) magnetic field [asymmetric hysteresis cycles (L. Ne´el, in Proceedings of the R. A. Welch Foundation Conference on Chemical Res. II, Atomic Structure, Houston, Texas, 1958)] after the sample has been cooled in a static fieldH(0≤H≤1.1 kOe). WhenH=0, the magnetizationmnin the field off state (h=0) grows as the logarithm of the number of cycles (n), while the magnetization in the on state (h≠0)Mndecreaseswith cycle number. This weaker response reflects an increase of the stiffness of the spin system after each cycle. At low temperaturemngrows linearly with temperature, reaches a maximum aroundT∼0.6Tgand decreases asTgis approached. The effects are larger when the system is prepared in a nonequilibrium state (rapid thermal quenching, or removal of the static fieldH). The irreversible growth of the magnetizationmnscale linearly withTg(i.e., exchange) for samples of 0.5 and 2.6 at. % Mn concentration. We find thatmngrows as the value ofHis increased, reaches a maximum aroundH∼Tg/15 and decreases slowly at higher fields. We suggest as a possible interpretation of this phenomenon, the existence of a cavity in the distribution of local fields acting on the low temperature excitations. Additional information on the role of anisotropic forces will also be presented.