The final version is available at: http://www.aanda.orgWe have performed simulations of the long-term evolution of the spin state of small active comet nuclei (1 km and 0.6 km) in the orbit of 46P/Wirtanen under the effect of the torque of the nongravitational force. A total of 46 combinations of irregular shapes and activity patterns have been simulated. We observe typical changes of the spin period of 0.01−10 h at each perihelion passage during the simulations, depending on the initial spin period and on the temporal evolution of the spin state. The direction of the angular momentum also changes by 0.1 to several tens of degrees per orbit. These changes are not always associated with an observable excitation of the spin state. While the nucleus gets to excited spin states in some simulations, it remains in a pure spin state during several tens of orbits in others. Therefore, even small and very active nuclei like 46P/Wirtanen could remain in their spin state of minimum energy (pure spin) during at least several tens of perihelion passages. We find that, for the parameters used in our simulation, a drastic increase in spin period to ∼200 h is required before the excitation of the spin state can occur. Further results and their consequences for the observations of rotational parameters of cometary nuclei are thoroughly described in the text.Peer reviewed