A TeV flare from the BL Lac object Mrk 421 was detected in May of 1994 by the Whipple Observatory air Cherenkov experiment during which the flux above 250 GeV increased by nearly an order of magnitude over a 2-day period. Contemporaneous observations by ASCA showed the X-ray flux to be in a very high state. We present these results, combined with the first ever simultaneous or nearly simultaneous observations at GeV gamma-ray, UV, IR, mm, and radio energies for this nearest BL Lac object. While the GeV gamma-ray flux increased slightly, there is little evidence for variability comparable to that seen at TeV and X-ray energies. Other wavelengths show even less variability. This provides important constraints on the emission mechanisms at work. We present the multiwavelength spectrum of this gamma-ray blazar for both quiescent and flaring states and discuss the data in terms of current models of blazar emission

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