The phenomenon of low-temperature homogenization (LTH) during interdiffusion is studied under condition a t Dv £ 2 / 1 ) ( (Dv is the bulk diffusion coefficient, a is the lattice parameter) using nano-objects of binary Cu-Ni and Cr-Ni systems compacted from nano-powders and produced by mechanical alloying. Two stages of LTH were detected: at the first stage (t £ 103 s) the volume fraction of solution rapidly grows; at the second stage (t > 103 s) the volume fraction of solutions grows slowly with practically constant average solution concentration. The first stage of LTH correlates with active grain growth caused by small size (l) of structural element and nonequilibrium structure of nano-objects. Obtained results are analyzed theoretically in terms of interdiffusion along migrating GBs due to grain growth at the first stage and DIGM mechanism at the second stage. It is shown that the GB concentration distribution during interdiffusion along migrating GBs and the kinetics of LTH depend on a parameter l/l where 2 / 1 ) / ( b b V sD d l= is the characteristic diffusion length. The mechanisms and criteria of LTH are proposed.