Dynamic behaviour is fundamental to life and a fascinating area of research is to try to uncover the molecular mechanisms responsible for the great variety of rhythmical patterns occurring in nature. In this article, we will review the programme of studies which we have undertaken on the temporal organisation of cells. There is overwhelming evidence that the reversible phosphorylation of proteins, mediated by kinases and phosphatases, influences virtually all aspects of cellular function, including proliferation, differentiation and neoplastic transformation. Our particular interest has been in studying protein phosphorylation and the expression of phosphoamino acid and phosphoprotein phosphatases in leukaemic cells, which can be induced to undergo differentiation in culture. We have demonstrated the existence of oscillations in protein expression and enzyme activity and have shown that the presence of inducers of differentiation can influence the rhythms with respect to mean, period and amplitude. Our findings suggest that regulation of the balance between protein phosphorylation and dephosphorylation may be achieved by modulation of oscillatory characteristics, and that this may be crucial to the control of cellular function and cell transformation.