The solar cosmic-ray event on 1990 May 24 can be divided into three phases: a first impulsive production of γ-rays and greater than 200 MeV neutrons; a second slower phase during which there were high-energy protons at the Sun for ~20 minutes producing pions and high-energy neutrons; and a third phase when the protons observed by the IMP 8 and GOES spacecraft and by neutron monitors were injected into interplanetary space. This third phase started after the onset of the event but before the second phase had ceased. We found that high-energy neutron production occurred during the last 60 s of the impulsive phase and at least the first 19 minutes of the second phase. During the second phase the high energy-neutron and γ-ray emissions decayed more slowly than either the 2.2 MeV or 4-7 MeV γ-ray line emissions. A two-component neutron energy spectrum that changes between the first and second phases gives a reasonable fit to the count rate increase recorded by the Climax neutron monitor. From the fit we infer that the integrated neutron emissivity at the Sun was ~3.5 × 1030 sr-1 for E > 100 MeV. The maximum intensity of P > 1.5 GV solar protons near the Earth was 4.5 × 103 (m2 sr s)-1. The differential solar proton energy flux (dJ/dE) as a function of rigidity at the Sun can be described by an evolving power-law spectrum. We estimate that the number of escaping protons with E > 30 MeV in the third phase was 7%-14% of the number of protons required to produce the solar neutron increase at the Earth. Although it is attractive to assume that the interplanetary solar protons simply leaked out from the trapping region at the Sun, the data suggest that the interplanetary solar protons were not from the population of energetic particles that produced the neutron and γ-ray emissions but were freshly accelerated during the third phase of the solar flare.