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(Abridged) We present a detailed analysis of week-long simultaneousobservations of the blazar Mrk421 at 2-60 keV X-rays (RXTE) and TeV gamma-rays(Whipple and HEGRA) in 2001. The unprecedented quality of this dataset enablesus to establish firmly the existence of the correlation between the TeV andX-ray luminosities, and to start unveiling some of its more detailedcharacteristics, in particular its energy dependence, and time variability. Thesource shows strong, highly correlated variations in X-ray and gamma-ray. Noevidence of X-ray/gamma-ray interband lag is found on the full week dataset (<3ks). However, a detailed analysis of the March 19 flare reveals that data arenot consistent with the peak of the outburst in the 2-4 keV X-ray and TeV bandbeing simultaneous. We estimate a 2.1+/-0.7 ks TeV lag. The amplitudes of theX-ray and gamma-ray variations are also highly correlated, and the TeVluminosity increases more than linearly w.r.t. the X-ray one. The strongcorrelation supports the standard model in which a unique electrons populationproduces the X-rays by synchrotron radiation and the gamma-ray component byinverse Compton scattering. However, for the individual best observed flaresthe gamma-ray flux scales approximately quadratically w.r.t. the X-ray flux,posing a serious challenge to emission models for TeV blazars. Rather specialconditions and/or fine tuning of the temporal evolution of the physicalparameters of the emission region are required in order to reproduce thequadratic correlation.

Multiwavelength Observations of Markarian 421 in March 2001: an Unprecedented View on the X-ray/TeV Correlated Variability