We have extended our model for charged current neutrino-nucleus interactions to neutral current reactions. For the elementary neutrino-nucleon interaction, we take into account quasielastic scattering, Delta excitation and the excitation of the resonances in the second resonance region. Our model for the neutrino-nucleus collisions includes in-medium effects such as Fermi motion, Pauli blocking, nuclear binding, and final-state interactions. They are implemented by means of the Giessen Boltzmann-Uehling-Uhlenbeck (GiBUU) coupled-channel transport model. This allows us to study exclusive channels, namely pion production and nucleon knockout. We find that final-state interactions modify considerably the distributions through rescattering, charge-exchange and absorption. Side-feeding induced by charge-exchange scattering is important in both cases. In the case of pions, there is a strong absorption associated with the in-medium pionless decay modes of the Delta, while nucleon knockout exhibits a considerable enhancement of low energy nucleons due to rescattering. At neutrino energies above 1 GeV, we also obtain that the contribution to nucleon knockout from Delta excitation is comparable to that from quasielastic scattering.