Large , high-energy ( E > 100 GeV ) cosmic neutrino telescopes are now quite mature .
IceCube , for example , observes about 50,000 well-reconstructed single atmospheric neutrino events/year , with energies above 100 GeV .
Although the neutrino detection probability is small , current detectors are large enough so that it is possible to detect two neutrinos from the same cosmic-ray interaction .
In this paper , we calculate the expected rate of double-neutrino interactions from a single cosmic-ray air shower .
The rate is small , about 0.07 events/year for a 1 km ^ { 3 } detector like IceCube , with only a small dependence on the assumed cosmic-ray composition and hadronic interaction model .
For a larger detector , like the proposed KM3Net , the rate is about 0.8 events/year , a rate that should be easily observable .
These double neutrino interactions are the major irreducible background to searches of pairs of particles produced in supersymmetric neutrino or cosmic-ray air-shower interactions .
Other standard-model backgrounds are considered , and found to be small .