Abstract: A multi-stage cryocooler has three or more stages, including an active first stage and passive second and third stages. The active stage may include a Stirling expander, and the passive second and third stages may be pulse tube coolers. The cryocooler may provide cooling at three different temperatures. The coldest cooling temperature may be at or below 10 K, and may be at or below 5 K. The system may provide cooling at such low temperatures while still operating at a relatively high frequency, for example, at a frequency of at least about 20 Hertz.