Double Rydberg states were populated by triple electron capture in collisions of highly charged ions with atoms. The highest stabilization of states produced by triple capture at y Х 0.2 a.u. was found for binding energies of the projectile electrons near the limits of the ͑2, n, n 0 ͒ and ͑3, n, n 0 ͒ series. Population of triply excited double Rydberg states was confirmed by the emission of Rydberg transitions. Results are interpreted by two successive autotransfer into Rydberg states for ͑3, n, n 0 ͒ states and of one-step two-electron autotransfer for ͑2, n, n 0 ͒ states. [S0031-9007(96)01692-4]