For many kinds of capital, depreciation rates change systematically with the age of the capital. Consider an example that captures essential aspects of human capital, both regarding its accumulation and its depreciation: a worker obtains knowledge in period 0, then uses this knowledge innproduction in periods 1 and 2, and thereafter retires. Here, depreciation accelerates: it occurs at a 100% rate after period 2, and at a lowe (perhaps zero) rate before that. The present paper analyzesnthe implications of non-constant depreciation rates for the optimal timing of taxes on capital income. The main finding is that under natural assumptions, the path of tax rates over time must be oscillatory. Oscillatory tax rates are optimal when depreciation rates accelerate with the age of the capital (as in the above example), and provided that the government can commit to the path ofnfuture tax rates but cannot apply different tax rates in a given year to different vintages of capital.