  We present unquenched lattice QCD results for the matrix elements of
four-fermion operators relevant to the description of the neutral K and D
mixing in the Standard Model and its extensions. We have employed simulations
with Nf = 2 + 1 + 1 dynamical sea quarks at three values of the lattice
spacings in the interval 0.06 - 0.09 fm and pseudoscalar meson masses in the
range 210 - 450 MeV. Our results are extrapolated to the continuum limit and to
the physical pion mass. Renormalization constants have been determined
non-perturbatively in the RI-MOM scheme. In particular, for the Kaon
bag-parameter, which is relevant for the \overline{K}^0-K^0 mixing in the
Standard Model, we obtain B_K^{RGI} = 0.717(24).
