The hyperfine-structure-interaction constants have been measured in the ground states of 18-min Br80 and 4.5-h Br80m. The method used was that of atomic-beam radio-frequency spectroscopy with radioactive detection. The results are: |a(Br80)|=323.9(4) Mc/sec, |b(Br80)|=227.62(10) Mc/sec with ab<0 and a(Br80m)=166.05(2) Mc/sec and b(Br80m)=-874.9(2) Mc/sec. The magnetic-dipole and electric-quadrupole moments of these isotopes were calculated from the measured interaction constants and known nuclear data for the stable Br isotopes; these moments are: |μI(Br80)|=0.5138(6) nm, |Q(Br80)|=0.199(8) b, QμI>0 μI(Br80m)=1.3170(6) nm, Q(Br80m)=0.76(3) b. The μI's are corrected for diamagnetic shielding and the Q's are corrected for core polarization effects.