We present analytic formulae for the QCD renormalization group factors relating the Wilson coefficients C_i(μ_t) and C_i(μ), with μ _t= O (m _t) and μ<μ_t, of the ΔF=2 dimension six four-quark operators Q_i in the Standard Model and in all of its extensions. Analogous analytic formulae for the QCD factors relating the matrix elements 〈Q_i(2 GeV)〉 and 〈Q_i(μ_K)〉 with μ_K<2 GeV are also presented. The formulae are given in the NDR scheme. The strongest renormalization-group effects are found for the operators with the Dirac structures (1−γ₅)⊗(1+γ₅) and (1−γ₅)⊗(1−γ₅). We calculate the matrix elements 〈 K ̄ ⁰|Q _i|K ⁰〉 in the NDR scheme using the lattice results in the LRI scheme. We give expressions for the mass differences ΔM_K and ΔM_B and the CP-violating parameter ϵ_K in terms of the non-perturbative parameters B_i and the Wilson coefficients C_i(μ_t). The latter summarize the dependence on new physics contributions.