Samples of 99.99 pct pure copper and nickel of 99.998 pct purity were deformed by highpressure torsion (HPT) at different hydrostatic pressures, to different shear strains. Activation enthalpies (Q) were determined by differential scanning calorimetry (DSC) using Kissinger's method. For the one annealing peak found in HPT Cu, Q amounts to Q = 0.78 to 0.48 eV depending on the shear strain applied. In the case of Ni, the activation enthalpies of the two annealing peaks were determined as Q = 0.65 eV and Q = 0.95 eV, respectively, with no obvious dependence on shear strain, although this has been indicated by the annealing peak temperatures. Applying defect specific analyses of the annealing peaks, it turned out that the larger Q value represents the annihilation of dislocations and agglomerates, while the smaller one reflects the annihilation of single or double vacancies. Concerning the strain dependence of the larger Q, two possible explanations have been discussed: (1) the annihilation of dislocations assisted by the strain-dependent density of vacancy agglomerates and (2) the annihilation of dislocations enhanced by a strain-dependent level of long-range internal stresses. Because of closer correlations of Q with external and internal stresses at very high shear strains, explanation (2) has been favored.