The coarsening of precipitates under applied stress has drawn attention since the early 70's, when the possibility of significant improvement of the yield strength of Ni-based alloys was demonstrated [1]. It was shown that aging under applied stress significantly biases evolution of the morphology of γ' (Ni 3 Al) precipitates, leading to rafting (directional coarsening). The kinetics of rafting has also being investigated, albeit sparingly [2][3][4]. In all the previous work, the specimens were initially aged under stress-free conditions to produce large γ' precipitates. The stress was then applied and evolution of the precipitate microstructure investigated. Moreover, the stresses were large enough to plastically deform the alloys. Evolution of the γ' precipitate microstructure under conditions of purely elastic deformation has not been previously investigated. Only recently have there been serious attempts to evaluate the kinetics of directional coarsening using computer simulation experiment [5][6][7][8].We have investigated the kinetics of the early stages of coarsening of γ' precipitates in Ni-13.36 Al [9,10] and Ni-12.92 Ge alloys (compositions in at. %). Single crystal samples were aged under compression at 640 °C (Ni-Al) and 625 °C (Ni-Ge), with the applied stress parallel to [001]. The maximum stresses, σ, used were ~150 MPa (Ni-Al) and ~100 MPa (Ni-Ge); the plastic strain was generally less then 1% for most of the specimens tested. The longest aging times were 1021 h (Ni-Al) and 288 h (Ni-Ge). The microstructures were examined by transmission electron microscopy, primarily in the section perpendicular to the applied stress. The morphology of the γ' precipitates was characterized by their aspect ratios and a shape parameter that provides a measure of how cuboidal they are. Rafting was not observed in either alloy, though the applied stress promotes the coalescence of γ' precipitates in the Ni-Al alloy. The very small difference between the stiffness constants of the precipitate and matrix phases in Ni-Al alloys suggests that the driving force for elastically-based rafting is negligibly small [10]. Compressive stress retards the kinetic of coarsening in both alloys; this is evident for Ni-Al alloys as shown in Fig. 1. The reduction in average size of the particles was in the range 12 to 25% depending on the alloy and the aging time. Data on the variation of the average radius, 〈r〉, as a function of aging time, t, were plotted in the form 〈r〉 3 vs. t to check the linearity of the relationship 〈r〉 3 ≈ kt [11,12], where k is the rate constant for coarsening. The results are reasonably linear for the Ni-Ge alloy over the entire range of stress; for the Ni-Al alloy it deviates from linearity at a stress of ~125 MPa and for the lower range of stress at aging times longer than about 300 h. The relationship 〈r〉 3 ∝ t at short aging times is consistent with predictions of some computer simulations [5,6], as is the deviation from linearity at longer times [8]. The slopes of the straight lines fitted to the data on ...