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We derive one-loop renormalization group equations (RGE's) for Yukawacoupling parameters of quarks and for the vacuum expectation values of theHiggs doublets in a general framework of the Standard Model with two Higgsdoublets (2HDM ``type III''). In the model, the neutral-Higgs-mediatedflavor-changing neutral currents are allowed but are assumed to be reasonablysuppressed at low energies. The popular ``type II'' and ``type I'' models arejust special cases of this framework. We also present a numerical example forthe RGE flow of Yukawa coupling parameters and masses of quarks. Detailedinvestigation, through RGE's, of connection between the low energy and the highenergy structure of these 2HDM's would give us some additional insights intothe viability of such frameworks, i.e., it would tell us for which choices ofphenomenologically acceptable values of low energy parameters such frameworkscan be regarded as reasonably natural (without excessive changes in theparameter structure as energy of probes increases over a wide range).Furthermore, such analyses could provide us with possible signals of newphysics at high energies.Comment: 26 pages(LaTeX), 13 Postscript figures, Acknowledgements correcte

ONE-LOOP RENORMALIZATION GROUP EQUATIONS OF THE GENERAL FRAMEWORK WITH TWO HIGGS DOUBLET