The time evolution of edge localized modes (ELMs) in the Joint European Torus tokamak [P. H. Rebut et al., Nucl. Fusion 25, 1011 (1985)] is investigated using the JETTO predictive modeling code [M. Erba et al., Plasma Phys. Controlled Fusion 39, 261 (1997)]. It is found that both pressure-driven ballooning and current-driven peeling modes can play a role in triggering the ELM crashes. In the simulations carried out, each large ELM consists of a sequence of quasicontinuous small ELM crashes. Each sequence of ELM crashes is separated from the next sequence by a relatively longer ELM-free period. The initial crash in each ELM sequence can be triggered either by a pressure-driven ballooning mode or by a current-driven peeling mode, while the subsequent crashes within that sequence are triggered by current-driven peeling modes, which are made more unstable by the reduction in the pressure gradient resulting from the initial crash. The HELENA and MISHKA ideal magnetohydrodynamic stability codes [A. B. Mikhailovskii et al., Plasma Phys. Rep. 23, 713 (1997)] are used to validate the stability criteria used in the JETTO simulations. This stability analysis includes infinite-n ideal ballooning, finite-n ballooning, and low-n kink/peeling modes.