  We derive one-loop renormalization group equations (RGE's) for Yukawa
coupling parameters of quarks and for the vacuum expectation values of the
Higgs doublets in a general framework of the Standard Model with two Higgs
doublets (2HDM ``type III''). In the model, the neutral-Higgs-mediated
flavor-changing neutral currents are allowed but are assumed to be reasonably
suppressed at low energies. The popular ``type II'' and ``type I'' models are
just special cases of this framework. We also present a numerical example for
the RGE flow of Yukawa coupling parameters and masses of quarks. Detailed
investigation, through RGE's, of connection between the low energy and the high
energy structure of these 2HDM's would give us some additional insights into
the viability of such frameworks, i.e., it would tell us for which choices of
phenomenologically acceptable values of low energy parameters such frameworks
can be regarded as reasonably natural (without excessive changes in the
parameter structure as energy of probes increases over a wide range).
Furthermore, such analyses could provide us with possible signals of new
physics at high energies.
