The authors present recent results on b-hadron lifetimes and mixing obtained from the analysis of the data collected at the Tevatron Collider by the CDF and D0 Collaborations in the period 2002-2004. Many lifetime measurements have been updated since the Summer 2004 conferences, sometimes improving significantly the accuracy. Likewise the measurement of the B{sub d} oscillation frequency has been updated. New limits on the B{sub s} oscillation frequency have been determined using for the first time Run II data.

The Tevatron collider at Fermilab provides a very rich environment for the study of b-hadrons. Both the D0 and CDF experiments have collected a sample of about 1 fb{sup -1}. they report results on three topics: b-hadron lifetimes, polarization amplitudes and the decay width difference in B{sub s}{sup 0} {yields} J/{psi}{phi}, and B{sub s}{sup 0} mixing.

The Tevatron experiments, CDF and D0, have produced a wealth of new B-physics results since the start of Run II in 2001. We've observed new B-hadrons, seen new effects, and increased many-fold the precision with which we know the properties of b-quark systems. In these proceedings, we will discuss two of the most fruitful areas in the Tevatron B-physics program: lifetimes and mixing. We'll examine the experimental issues driving these analyses, present a summary of the latest results, and discuss prospects for the future.

This short review reports on recent results from CDF and D0 experiments at the Tevatron collider on B°{sub s} mixing and the lifetimes of B°{sub s} and [Lambda]{sub b}.

Precision B-physics results from the CDF and DO Collaborations based on data collected during the Tevatron 1992-96 run are presented. In particular we discuss the measurement of B hadron lifetimes, and B° - {anti B}° mixing results obtained using time- evolution analyses. Perspectives for the next Tevatron run, starting in 1999, are also reported.