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Restrictions on primaries responsible for correlated muon events at Soudan.

We analyze the properties necessary for the primary cosmic rays responsible for the multiple-muon showers observed to be coming from set sidereal directions by the Soudan proton-decay detector. We find that the flux of such events requires that the primaries be hadronic and specifically excludes the possibility that ..gamma.. rays are responsible for these events. We show that if neutrons are responsible for these events, the finite lifetime of the neutron limits the distance of their sources from the Earth to 50 pc or less. Exotic neutrals would have to have lifetimes longer than that of the neutrons. Observation of a time-dependent flux implies an upper limit to the mass of the primary. We show that charged primaries cannot reach the Earth from reasonable distances even if originally emitted in rather tight beams and even if the beams rotate through the magnetic-field direction and propagate down the field to the Earth.