The Polycomb (PcG) and Trithorax (TrxG) group proteins work antagonistically on several hundred developmentally important target genes, giving stable mitotic memory, but also allowing flexibility of gene expression states. How this is achieved in quantitative terms is poorly understood. Here, we present a quantitative kinetic analysis in living Drosophila of the PcG proteins Enhancer of Zeste, (E(Z)), Pleiohomeotic (PHO) and Polycomb (PC) and the TrxG protein absent, small or homeotic discs 1 (ASH1). Fluorescence recovery after photobleaching and fluorescence correlation spectroscopy reveal highly dynamic chromatin binding behaviour for all proteins, with exchange occurring within seconds. We show that although the PcG proteins substantially dissociate from mitotic chromatin, ASH1 remains robustly associated with chromatin throughout mitosis. Finally, we show that chromatin binding by ASH1 and PC switches from an antagonistic relationship in interphase, to a cooperative one during mitosis. These results provide quantitative insights into PcG and TrxG chromatin-binding dynamics and have implications for our understanding of the molecular nature of epigenetic memory.