  I first discuss the phenomenology of a^q_fs (q=d,s), which is the CP
asymmetry in flavour-specific B_q decays such as B_d -> X l^+ nu-bar_l or B_s
-> D_s^- pi^+. a^q_fs can be obtained from the time evolution of any untagged
B_q decay. Then I present recently calculated next-to-leading-order QCD
corrections to a_fs^q, which reduce the renormalisation scheme uncertainties
significantly. For the Standard Model we predict a^d_fs=-(5.0 +/- 1.1)*10^(-4)
and a^s_fs= (2.1 +/-0.4)*10^-5. As a by-product we determine the ratio of the
width difference in the B_d system and the average B_d width to (Delta
Gamma_d)/Gamma_d = (3.0 +/- 1.2)*10^(-3) at next-to-leading order in QCD.
