The BL Lac object Mkn~421 was observed three times by the X-ray observatory BeppoSAX in consecutive days during 1997 April and May. The source was in a quiescent state, with an average 2-10 keV flux of 9.0 x 10^(-11) erg/cm/cm/s. Flux variation by a factor of ~2 on timescales as short as a few 10 ks were more pronounced in the hard (i.e. above ~3 keV) than in the soft X-rays. The broadband (0.1-40 keV) spectrum is concave and can be most easily explained with a power-law model which steepens gradually with energy. In this framework, neither photoabsorption edges nor resonant absorption lines are required, strengthening the case against the ubiquity of such features in BL Lac objects, which had been previously suggested by Einstein observations. The broadband spectrum hardens with hard X-ray flux, mostly due to a flattening above ~4 keV. This suggests that the relativistic highest energy electron distribution properties drive the X-ray spectral dynamics: either a stratification of the distribution in the jet with energy or inhomogeneities in the electron injection mechanism could be consistent with the observed variability pattern.
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