Desmosomes, strong cell-cell junctions of epithelia and cardiac muscle, link intermediate filaments to cell membranes and mechanically integrate cells across tissues, dissipating mechanical stress. They comprise 5 major protein classes - desmocollins and desmogleins (the desmosomal cadherins), plakoglobin, plakophilins and desmoplakin - whose individual contribution to the structure and turnover of desmosomes is poorly understood. Using live-cell imaging together with FRAP and FLAP we show that desmosomes consist of two contrasting protein fractions or modules: a very stable desmosomal core of desmosomal cadherins and plakoglobin, and a highly mobile plakophilin. As desmosomes mature from calcium-dependence to calcium-independent hyper-adhesion, core stability increases, but Pkp2a remains highly mobile. Desmoplakin is initially mobile but stabilises with hyper-adhesion. We show that desmosome down-regulation during growth factor-induced cell scattering proceeds by internalisation of whole desmosomes, which still retain a stable core and highly mobile Pkp2a. This molecular mobility of Pkp2a suggests a transient and probably regulatory role for Pkp2a in the desmosome.