Many central banks in developed countries have had very low policy rates for quite some time. A growing number are experimenting with official rates that are negative. We develop a New Keynesian model in which the zero lower bound (ZLB) on nominal interest rates is imposed as an occasionally binding constraint and use this model to examine the duration of ZLB episodes. In addition, we show that capital accumulation and capital adjustment costs can raise significantly the length of time an economy spends at the ZLB, as can the conduct of monetary policy. We identify anticipation effects that make the ZLB more likely to bind and we show that allowing negative nominal interest rates shortens average durations, but only by about one quarter.