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In 2008, the blazar Mrk421 entered in a very active phase and was one of thebrightest sources in the sky at TeV energies, showing strong and frequentflaring. We searched for gamma-ray emission at energies E > 0.8 TeV during thewhole 2008 with the ARGO-YBJ experiment, a full coverage air shower detectorlocated at Yangbajing (4300 m a.s.l., Tibet, P.R. China). The observed signalis not constant and in correlation with X-ray measurements. The averageemission, during the active period of the source, was about twice the CrabNebula level, with an integral flux of (4.9$\pm 2.0$)x 10$^{-11}$ photonscm$^{-2}$ s$^{-1}$ for E$_{\gamma}$ >1 TeV.  This paper concentrates on 2008 June when the Mrk421 flaring activity hasbeen studied from optical to 100 MeV gamma rays, and only partially up to TeVenergies, since the moonlight hampered the Cherenkov telescope observationsafter 8 June. Our data complete these observations, with the detection of asecond flare of intensity of about 7 Crab units on June 11-13, with astatistical significance of 4.2 standard deviations. The observed flux isconsistent with a prediction made in the framework of the SynchrotronSelf-Compton model, in which the flare is caused by a rapid acceleration ofleptons in the jet.

Gamma-Ray Flares from Mrk421 in 2008 observed with the ARGO-YBJ experiment