We present the results of a multiwavelength campaign for Mrk 501 performed in March 1996 with ASCA, EGRET, Whipple, and optical telescopes. In the X-ray band, a spectral break was observed around 2 keV. We report here for the first time the detection of high-energy gamma-ray flux from Mrk 501 with EGRET with 3.5 sigma significance (E>100 MeV). Higher flux was also observed in April/May 1996, with 4.0 sigma significance for E>100 MeV, and 5.2 sigma significance for E>500 MeV. The gamma-ray spectrum was measured to be flatter than most of the gamma-ray blazars. We find that the multiband spectrum in 1996 is consistent with that calculated from a one-zone SSC model in a homogeneous region. In the context of this model, we investigate the values of the magnetic field strength and the beaming factor allowed by the observational results. We compare the March 1996 multiwavelength spectrum with that in the flare state in April 1997. Between these two epochs, the TeV flux increase is well correlated with that observed in keV range. The keV and TeV amplitudes during the April 1997 flare are accurately reproduced, assuming that the population of synchrotron photons in 1996 are scattered by the newly injected relativistic electrons, having maximum energies of G_max = 6.0e6. However, the TeV spectrum observed during March 1996 campaign is flatter than predicted by our models. We find that this cannot be explained by either higher order Comptonization or the contribution of the `seed IR photons from the host galaxy for the first-order external radiation Comptonization.
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