Oscillations of B0s mesons have been studied in samples selected from about 3.5 million hadronic Z decays detected by DELPHI between 1992 and 1995. One analysis uses events in the exclusive decay channels: B0s -> Ds- pi+ or Ds- a1+ and B0s -> anti-D0 K- pi+ or anti-D0 K- a1+, where the D decays are completely reconstructed. In addition, B0s anti-B0s oscillations have been studied in events with an exclusively reconstructed Ds accompanied in the same hemisphere by a high momentum hadron of opposite charge. Combining the two analyses, a limit on the mass difference between the physical B0s states has been obtained: Delta(m_B0s) > 4.0 ps^{-1} at the 95% C.L. with a sensitivity of Delta(m_B0s) = 3.2 ps^{-1}. Using the latter sample of events, the B0s lifetime has been measured and an upper limit on the decay width difference between the two physical B0s states has been obtained: tau(B0s) = 1.53^{+0.16}_{-0.15}(stat.) +/- {0.07}(syst.) ps \Delta\Gamma(B0s)/\Gamma(B0s) < 0.69 at the 95% C.L. The combination of these results with those obtained using Ds+- lepton-+ sample gives: Delta(m_B0s) > 4.9 ps^{-1} at the 95% C.L. with a sensitivity of Delta(m_B0s) = 8.7 ps^{-1}. tau(B0s) = 1.46 +/- 0.11 ps and \Delta\Gamma(B0s)/\Gamma(B0s) < 0.45 at the 95% C.L.