We report a direct measurement of D0-D0 mixing parameters through a time-dependent amplitude analysis of the Dalitz plots of D(0) → K(S)(0) π+ π- and, for the first time, D0 → K(S)(0)K+ K- decays. The low-momentum pion π(s)(+) in the decay D*+ → D0 π(s)(+) identifies the flavor of the neutral D meson at its production. Using 468.5 fb(-1) of e+ e- colliding-beam data recorded near square root(s)=10.6 GeV by the BABAR detector at the PEP-II asymmetric-energy collider at SLAC, we measure the mixing parameters x = [1.6 ± 2.3(stat) ± 1.2(syst) ± 0.8(model)] × 10(-3), and y = [5.7 ± 2.0(stat) ± 1.3(syst) ± 0.7(model)] × 10(-3). These results provide the best measurement to date of x and y. The knowledge of the value of x, in particular, is crucial for understanding the origin of mixing.