  In this talk we present a calculation of the dacay rate difference in the
neutral $B_s-\bar{B}_s$ system, $\Delta \Gamma_{B_s}$, in next-to-leading order
(NLO) QCD. We find a sizeable decrease compared to leading-order (LO)
estimates: $ (\Delta \Gamma/\Gamma)_{B_s} = (f_{B_s}/210 MeV)^2 [0.006 B(m_b) +
0.150 B_S(m_b) - 0.0063]$ in terms of the bag parameters $B$ and $B_S$ in the
NDR scheme. We put special emphasize on the theoretical and physical
implications of this quantity.
