It is shown that, although the fermionic and scalar sectors of multi-Higgs-doublet models are not independent of each other, the fermion mass matrices, in particular, are invariant under the equiva lence class transformations of the scalar doublets. In light of this observation, a method originally formulated for counting the observable parameters of the Yukawa Lagrangian of the standard model is extended to count the observable parameters of the fermion mass matrices in multi-Higgs-doublet models. Completely different Yukawa coupling mass matrices may lead to the same set of physical observables.ll This is due to the invariance of the Lagrangian under the equivalence class transformations of a global group. In the standard model of electroweak interactions, one does not need to consider the Higgs potential when one determines this group. The subgroup of this group which preserves the forms of Yukawa coupling matrices, in turn, can be used to count the observable parameters of the Yukawa Lagrangian. 2 >.s> However, in the multi-Riggs-doublet extensions of the standard modeVH> one should consider the Higgs potential as well when one studies the Yukawa sector. This is because some of the parameters in the Higgs potential may be carried to the Yukawa sector by transforming the Higgs doublets under a unitary transformation and vice versa. Furthermore in these models, unlike in the standard model, the symmetries of the Y ukawa coupling matrices before and after the spontaneous symmetry breaking are not the same since the vacuum expecta tion values enter into the Yukawa coupling matrices after the spontaneous symmetry breaking as additional parameters. In this paper we study multi-Riggs-doublet models in the light of the above considerations. First we find that, although, in general, one must consider the sym metries of the Higgs potential as well when one determines the observable parameters of Yukawa Lagrangian, one does not need to consider the symmetries of the Higgs potential when one determines the observable parameters of the fermion mass matrices in particular since the fermion mass matrices are invariant under the equivalence class transformation of the scalar doublets. Then we examine how to find the global group which is used to count the observable parameters of the fermion mass matrices. We give some examples and a general analysis. One may write the Yukawa Lagrangian of a general k-Higgs-doublet version of the standard model as