We have developed a numerical algorithm to model the future collisional evolution of the low-orbiting Earth debris population, accounting for both the wide spectrum of masses (or sizes) of the orbital objects, and their different altitudes, which result in a variable efficiency of the drag-induced decay. The evolution process has been assumed to be caused by a number of source and sink mechanisms, such as launches, explosions, atmospheric drag, and mutual collisions. The collisional outcomes have been described through a semiempirical model for the fragment mass distributions, consistent with the available experimental evidence. A runaway exponential growth of collision fragments is always found in our model. Although its timing and pace are sensitive to some poorly known parameters, fairly plausible parameter choices predict that the runaway growth will occur within the next century, starting in the crowded shells between 700 and 1000 km of altitude and, somewhat later, between 1400 and 1500 km. The runaway growth is delayed until a few centuries in the future only if the catastrophic breakup threshold in specific impact energy for orbiting objects exceeds that for natural rocky bodies by at least a factor of 10. Our simulations show that the sensitivity of the results to future launch and/or deorbiting and removal policies is rather weak, so that drastic measures will need to be taken soon in order to significantly avoid or delay a catastrophic outcome. ¿ American Geophysical Union 1994