  Anticipating the important role of tree level FCNC processes in the indirect
search for new physics at distance scales as short as 10^-19-10^-21 m, we
present complete NLO QCD corrections to tree level Delta F=2 processes mediated
by heavy colourless gauge bosons and scalars. Such contributions can be present
at the fundamental level when GIM mechanism is absent as in numerous Z' models,
gauged flavour models with new heavy neutral gauge bosons and Left-Right
symmetric models with heavy neutral scalars. They can also be generated at one
loop in models having GIM at the fundamental level and MFV of which Two-Higgs
Doublet models with and without SUSY are the best known examples. In models
containing vectorial heavy fermions that mix with the standard chiral quarks
and models in which Z and SM neutral Higgs H mix with new heavy gauge bosons
and scalars also tree-level Z and SM neutral Higgs contributions to Delta F=2
processes are possible. In all these extensions new local operators are
generated having Wilson coefficients that are generally much stronger affected
by RG QCD effects than it is the case of the SM operators. The new aspect of
our work is the calculation of O(alpha_s) corrections to matching conditions
for the Wilson coefficients of the contributing operators in the NDR-MS scheme
that can be used in all models listed above. This allows to reduce certain
unphysical scale and renormalization scheme dependences in the existing NLO
calculations. We show explicitly how our results can be combined with the
analytic formulae for the P_i^a QCD factors that include both hadronic matrix
elements of contributing operators and RG evolution from high energy to low
energy scales. For the masses of heavy gauge bosons and scalars O(1)TeV the
remaining unphysical scale dependences for the mixing amplitudes are reduced
typically from 10-25%, depending on the operator considered, down to 1-2%.
