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.

6 pages with 5 figures