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 t
he first ever simultaneous or nearly simultaneous observations at GeV
gamma-ray, UV, IR, mm, and radio energies for this nearest BL Lac obje
ct. While the GeV gamma-ray flux increased slightly, there is little e
vidence for variability comparable to that seen at TeV and X-ray energ
ies. Other wavelengths show even less variability. This provides impor
tant constraints on the emission mechanisms at work. We present the mu
ltiwavelength spectrum of this gamma-ray blazar for both quiescent and
flaring states and discuss the data in terms of current models of bla
zar emission.