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The abstract of "Rare decay modes of the K mesons in gauge theories" Rare decay modes of the kaons such as K —jLfp, K —7(vl, K-yy, K —~p, and K —~ee are of theoretical interest since here we are observing higher-order weak and electro- magnetic interactions. Recent advances in unified gauge theories of weak and electromag- netic interactions allow in principle unambiguous and finite predictions for these processes. The above processes, which are "induced" icosi =1 transitions, are a, good testing ground for the cancellation mechanism first invented by Glashow, Iliopoulos, and Maiani (GIM) in order to banish l&S~=1 neutral currents. The experimental suppression of Kz —pP and nonsup- pression of Kz —pp must find a natural explanation in the GIM mechanism which makes use of extra quark(s). The procedure we follow is the following: We deduce the effective inter- action Lagrangian for ~+K-l+l and ~ +%-p+y in the free-quark model...