We provide multi-factor real option models (and quasi-analytical solutions) for equipment capital budgeting under uncertainty, when there is either unexpected, or anticipated, or uncertain (volatile) technological progress. We calculate the threshold level of revenues and operating costs using the incumbent equipment that would justify replacement. Replacement is deferred for lower revenue thresholds. If progress is anticipated or highly uncertain, alert financial managers should wait longer before replacing equipment. Replacement deferral increases with decreases in the expected correlation between revenue and operating costs, and with increases in the revenue and/or operating cost volatility. Uncertain technological progress increases the real option value of waiting. The best approach for equipment suppliers is to reduce the expected revenue and/or cost volatility, and/or reduce the expected uncertainty of technological innovations, since then an incentive exists for the early replacement of old equipment when a technologically advanced version is launched.