Constraints on the Cosmic Rays in the Small Magellanic Cloud

We show that recent $\gamma$-ray observations of the Small Magellanic Cloud with EGRET rule out a universal cosmic ray flux only at energies below $\approx 10$ GeV, while the observed diffuse X-ray and $\gamma$-ray background radiations have already ruled out, by more than three orders of magnitude, a universal extragalactic cosmic ray flux identical to that observed in the local solar neighborhood at energies below $10^6$ GeV.