  We write down the renormalization-group equations for the Yukawa-coupling
matrices in a general multi-Higgs-doublet model. We then assume that the
matrices of the Yukawa couplings of the various Higgs doublets to right-handed
fermions of fixed quantum numbers are all proportional to each other. We
demonstrate that, in the case of the two-Higgs-doublet model, this
proportionality is preserved by the renormalization-group running only in the
cases of the standard type-I, II, X, and Y models. We furthermore show that a
similar result holds even when there are more than two Higgs doublets: the
Yukawa-coupling matrices to fermions of a given electric charge remain
proportional under the renormalization-group running if and only if there is a
basis for the Higgs doublets in which all the fermions of a given electric
charge couple to only one Higgs doublet.
