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Multiple redundancy is a very complex form of redundancy about which little is known. This correspondence shows by construction that redundancy of any multiplicity can exist in an arbitrary combinational circuit, and that redundancy of any multiplicity ≥ 4 can exist in a tree circuit. Many examples are given. The correspondence concludes with a discussion of the effect multiple redundancy can have on multiple fault testing. It is shown that with a proper algorithm multiple redundancy can actually cause fewer problems than single redundancy does when single fault testing is being considered.