In this paper we present the results of simultaneous observations of the TeV blazar Markarian 421 ( Mrk 421 ) at X-ray and TeV gamma-ray energies with the Rossi X-Ray Timing Explorer ( RXTE ) and the stereoscopic Cherenkov Telescope system of the HEGRA ( High Energy Gamma Ray Astronomy ) experiment , respectively .
The source was monitored from February 2nd to February 16th and from May 3rd to May 8th , 2000 .
In both energy bands several flares with very rapid flux variability were observed .
In the X-ray band , the flux increased and decreased with e-folding times as short as about 5 hrs .
The 3-20 keV photon index varied between values of 2.2 and 2.9 .
For 5 pointings the data shows statistically significant evidence for spectral curvature .
The photon index varied substantially on very short time scales : on February 11th it hardened within 1.6 hrs by \Delta \Gamma = 0.18 and on February 14th it softened within 1.6 hrs by \Delta \Gamma = 0.2 .
The TeV observations of February 7th/8th showed statistically significant evidence for substantial TeV flux variability on 30 min time scale .
The TeV energy spectrum averaged over all the observations of the campaign shows a similar steep slope as in earlier HEGRA observations : dN / dE = N _ { 0 } \cdot ( E / 1 TeV ) ^ { - \Gamma } with N _ { 0 } = ( 25 \pm 1 _ { stat } ) \cdot 10 ^ { -12 } photons cm ^ { -2 } s ^ { -1 } TeV ^ { -1 } and \Gamma = 2.94 \pm 0.06 _ { stat } .
Within statistical errors no evidence for a curvature of the TeV energy spectrum is found .
We show the results of modeling the data with a time dependent homogeneous Synchrotron Self-Compton ( SSC ) model .
The X-ray and TeV gamma-ray emission strengths and energy spectra together with the rapid flux variability strongly suggest that the emission volume is approaching the observer with a Doppler factor of 50 or higher .
The different flux variability time scales observed at X-rays and TeV Gamma-rays indicate that a more detailed analysis will require inhomogeneous models with several emission zones .