  We discuss possible realizations of the hypothesis that all the fundamental
interactions of the elementary particles should be of gauge type, including the
Yukawa and Higgs ones. In the minimal SUSY extension of the standard model,
where the quartic Higgs couplings are ``gauged'' through the D-terms, it is
also possible to generate radiatively the Yukawa matrices for the light
generations, thus expressing them as functions of gauge couplings. The program
can also be applied to the SUSY LR model, where the possibility to induce
radiatively the mixing angles, can help to make viable the parity solution to
the strong CP problem. The superpotential of the model still includes some
non-gauge couplings, namely, the Yukawa for the third generation and the
trilinear terms involving the Higgs bi-doublet and two pairs of doublets.
Additional progress to relate these parameters to gauge couplings, can be made
by embedding the LR model within a SUSY model SU(4)_WxU(1)_{B-L} in five
dimensions, where the Higgs bi-doublet is identified as the extra component of
the 5D gauge field.
