  The measurements of Rb = sigma(e+e- -> bb~)/sigma(e+e- -> qq~) and of the b
quark forward-backward charge asymmetry, A^b_fb, at centre-of-mass energies
above the Z pole are described. The measurement of Rb is performed at \root{s}
between 130 and 189 GeV using a b-tagging method that exploits the relatively
large decay length of b-hadrons. The measurement of A^b_fb is performed using
the large statistics event sample collected at \root{s}=189 GeV with a
lepton-tag analysis based on the selection of prompt muons and electrons. The
results at \root{s}=189 GeV are: Rb = 0.163 +/- 0.013 (stat.) +/- 0.005
(syst.), A^b_fb = 0.61 +/- 0.18 (stat.) +/- 0.09 (syst.).
