We present the ETMC results for the bag parameters describing the neutral kaon mixing in the Standard Model and beyond and preliminary results for the bag parameters controlling the short distance contributions in the D^0-bar{D}^0 oscillations. We also present preliminary results for the B_{Bd}, B_{Bs}, B_{Bs}/B_{Bd} and xi -parameter controlling B^0_-bar{B}^0 oscillations in the Standard Model employing the so-called ratio method. Using Nf=2 maximally twisted sea quarks and Osterwalder-Seiler valence quarks we achieve both O(a)-improvement and continuum like renormalization pattern. Simulations are performed at three-values of the lattice spacing and several values of quark masses in the light, strange, charm region and above charm up to ~2.5m_c. Our results are extrapolated to the continuum limit and extrapolated/interpolated to the physical quark masses.
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