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The very-high-energy (VHE) ?-rays from BL Lac object Mrk 421 were observed with the twin stereoscopic Cerenkov system GT-48 in 2003. The observations in April–May have revealed a directional excess of VHE ? quanta with a statistical significance 5.46s. The observed source was located within 0°.1 of the coordinates of Mrk 421. Evidence for similar source emission behaviour of X-rays is correspondingly seen in nearly simultaneous data obtained from the all-sky monitor of the Rossi X-ray Timing Explorer. In the high-energy state of the object at E > 1 TeV, the source emission exceeded the relatively quiescent state by nearly three times and coincided within about 1.5 days with increased activity in the 2–10 keV energy band.