Asymmetric comas and repetitive appearances of structures in the heads and tails of comets are used to infer nuclei rotation periods. However, periodic behaviour of optically-thick expanding comas or of ion plasma production may contribute spurious results. The spin periods of comets are longer than those of asteroids, ranging generally over 10-100 h and above probable limits for gravitational escape. The periods show a flatter distribution, which may reflect an accretional rather than collisional-fragmentation history. Arguments for spin-up with age due to sublimating gases are weak; the converse is possible and spin-down due to preferential escape of particles from equatorial regions appears likely.