  We present recent results for the prediction of the Bs lifetime difference
from lattice Heavy Quark Effective Theory simulations. In order to get a
next-to-leading order result we have calculated the matching between QCD and
HQET and the two-loop anomalous dimensions in the HQET for all the \Delta B=2
operators, in particular for the operators which enter the width difference. We
present results from quenched and, for the first time, from unquenched
simulations. We obtain for the Bs lifetime difference,
(\Delta\Gamma_Bs/\Gamma_Bs)^{(que.)}=(5.1+/- 1.9+/- 1.7)10^(-2) and
(\Delta\Gamma_Bs/\Gamma_Bs)^{(unq.)}=(4.3+/- 2.0+/- 1.9)10^(-2) from the
quenched and unquenched simulations respectively
