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Brown dwarfs are massive analogs of extrasolar giant planets and may host types of atmospheric circulation not seen in the solar system. We analyzed a long-term Spitzer Space Telescope infrared monitoring campaign of brown dwarfs to constrain cloud cover variations over a total of 192 rotations. The infrared brightness evolution is dominated by beat patterns caused by planetary-scale wave pairs and by a small number of bright spots. The beating waves have similar amplitudes but slightly different apparent periods because of differing velocities or directions. The power spectrum of intermediate-temperature brown dwarfs resembles that of Neptune, indicating the presence of zonal temperature and wind speed variations. Our findings explain three previously puzzling behaviors seen in brown dwarf brightness variations., (Copyright © 2017 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works.)