  We conducted a multi-frequency campaign for the TeV blazar Mrk~421 in 1998
April. The campaign started from a pronounced high amplitude flare recorded by
SAX and Whipple; ASCA observation started three days later. In the X-ray data,
we detected multiple flares, occuring on time scales of about one day. ASCA
data clearly reveal spectral variability. The comparison of the data from ASCA,
EUVE and RXTE indicates that the variability amplitudes in the low energy
synchrotron component are larger at higher photon energies. In TeV Gamma-rays,
large intra-day variations -- which were correlated with the X-ray flux -- were
observed when results from three Cherenkov telescopes are combined. The RMS
variability of TeV Gamma--rays was similar to that observed in hard X-rays,
above 10 keV. The X-ray light curve reveals flares which are almost symmetric
for most of cases, implying the dominant time scale is the light crossing time
through the emitting region. The structure function analysis based on the
continuous X-ray light curve of seven days indicates that the characteristic
time scale is ~0.5 day. The analysis of ASCA light curves in various energy
bands appears to show both soft (positive) and hard (negative) lags. These may
not be real, as systematic effects could also produce these lags, which are all
much smaller than an orbit. If the lags of both signs are real, these imply
that the particle acceleration and X-ray cooling time scales are similar.
