The paper examines the precessional behaviour of spins in a binary, modelled as a system of three non-dissipatively coupled angular momenta, namely the orbital angular momentum and the two spin angular momenta. The model problem of three precessionally coupled angular momenta is considered in some generality. It is found that the precessional behaviour consists of a periodic nutation superimposed on an overall precession of the system about the axis of total angular momentum. Attention is focused on precession in close binaries containing compact objects, including the binary pulsar PSR 1913 + 16 and the Martin & Rees binary model of SS 433; it is shown that nutation in such systems will generally be too small to be observable.