  We compute the next-to-leading order QCD corrections to the off-diagonal
elements of the decay-width matrix Gamma entering the neutral B-meson
oscillations. From this calculation the width differences DeltaGamma and the CP
violation parameters (q/p) of Bd and Bs mesons are estimated, including the
complete O}(alpha_s) QCD corrections and the 1/mb contributions. For the width
difference DeltaGamma_s we agree with previous results. By using the lattice
determinations of the relevant hadronic matrix elements we obtain the
theoretical predictions DeltaGamma_d/Gamma_d=(2.42+-0.59) x 10^(-3) and
DeltaGamma_s/Gamma_s=(7.4+-2.4) x 10^(-2). For the CP violation parameters, we
find |(q/p)_d|-1=(2.96+-0.67) x 10^(-4) and |(q/p)_s|-1=(-1.28+-0.27) x
10^(-5). These predictions are compatible with the experimental measurements
which, however, suffer at present from large uncertainties.
