Abstract: We report on a measurement of the flavor-specific B-s(0) lifetime and of the D-s(-) lifetime using proton-proton collisions at center-of-mass energies of 7 and 8 TeV, collected by the LHCb experiment and corresponding to 3.0 fb(-1) of integrated luminosity. Approximately 407 000 B-s(0) -> D-s(()*()) -> D-s(()*()-) mu+v(mu) decays are partially reconstructed in the K+K-pi(-)mu(+) final state. The B-s(0) and D-s(-) natural widths are determined using, as a reference, kinematically similar B-0 -> Dd(*)(-) mu+v(mu) decays reconstructed in the same final state. The resulting differences between widths of B-s(0) and B-0 mesons and of D-s(-) and D- mesons are Delta(Gamma)(B) = -0.0115 +/- 0.0053(stat) +/- 0.0041 (syst) ps(-1) and Delta(Gamma)(D) = 1.0131 +/- 0.0117(stat) +/- 0.0065(syst) ps(-1), respectively. Combined with the known B-0 and D- lifetimes, these yield the flavor-specific B-s(0) lifetime, tau(fs)(Bs0) = 1.547 +/- 0.013 (stat) +/- 0.010 (syst) +/- 0.004(tau(B)) ps and the D-s(-) lifetime, tau(Ds-) = 0.5064 +/- 0.0030(stat) +/- 0.0017(syst) +/- 0.0017(sys) +/- 0.0017(tau(D)). The last uncertainties originate from the limited knowledge of the B-0 and D- lifetimes. The results improve upon current determinations.