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Major solar eruptions can accelerate protons up to relativistic energies. Solar relativistic ions arriving at 1 au may cause a solar particle event detectable by the worldwide network of neutron monitors (NMs), a ground-level enhancement (GLE) event. Using the newly computed NM yield function, we have fitted the 15 historic GLEs. Moments of the fitted proton distributions are used for the analysis. Profiles of the proton net flux are very diverse, while some profiles are similar. For this study, we select two events with similar time profiles, GLE 60 (2001 April 15) and GLE 65 (2003 October 28), and ask what makes these GLEs similar. We compare the GLEs with their progenitor solar flares and coronal mass ejections (CMEs). We find a close relationship between the rise and peak of the GLE, on the one hand, and the solar flare and the metric radio emissions from extended coronal sources at the base of the CME, on the other hand. The GLE decay time, the rate of the proton spectrum evolution, and the CME speed are proportional to the duration of the soft X-ray flare. We compare the two GLEs with GLE 59 (2000 July 14) analyzed by Klein et al. and with the deka-MeV nucleon ^−1 proton and helium data from the ERNE instrument on the Solar and Heliospheric Observatory spacecraft. The comparison indicates that a single solar eruption can produce more than one component of solar energetic particles, differently contributing at different energies and locations.