A dynamical model of edge-localized mode (ELM) phenomena is presented. It combines the paradigms of the L - H transition mediated by electric field shear induced suppression and generation with a simplified description of MHD instability and with a transport analysis of the plasma edge. In the parameter regime characteristic of an H-mode plasma, the model exhibits a transition to stationary relaxation oscillations (i.e. stable limit cycle behaviour) corresponding to ELMs. The dependence of ELM frequency, amplitude etc on the heating power and other control parameters is studied.