The mammalian cell nucleus contains numerous sub-compartments, which have been implicated in essential processes such as transcription and splicing. The mechanisms by which nuclear compartments are formed and maintained are unclear. More fundamentally, it is not known how proteins move within the cell nucleus. We have measured the kinetic properties of proteins in the nucleus of living cells using photobleaching techniques. Here we show that proteins involved in diverse nuclear processes move rapidly throughout the entire nucleus. Protein movement is independent of energy, which indicates that proteins may use a passive mechanism of movement. Proteins rapidly associate and dissociate with nuclear compartments. Using kinetic modelling, we determined residence times and steady-state fluxes of molecules in two main nuclear compartments. These data show that many nuclear proteins roam the cell nucleus in vivo and that nuclear compartments are the reflection of the steady-state association/dissociation of its 'residents' with the nucleoplasmic space. Our observations have conceptual implications for understanding nuclear architecture and how nuclear processes are organized in vivo.