Recent experimental data seem to indicate that there is significant structure in the cosmic ray spectrum above 1018 electron volts (eV). Besides a dip at ∼5 × 1018 eV, two events above 2 × 1020 eV have been observed. The implications for the existence of the Greisen-Zatsepin-Kuzmin cutoff, a long-lasting and still open question in cosmic ray physics, are discussed. This cutoff at a few times 1019 eV, caused by energy losses in the cosmic microwave background, has been predicted to occur in most acceleration models involving extragalactic sources. An acceleration origin of particles above 1020 eV within a few megaparsecs cannot be ruled out yet. However, persistence of the apparent gap in the existing data at a quadrupled total exposure would rule out many acceleration models at the 99 percent confidence level for any source distance. Particles above 1020 eV might then be directly produced by decay from some higher energy scale in contrast to acceleration of charged particles.