Consensus trees provide a means of representing cladistic information that is common to a set of fundamental trees. An analysis of the logical relations that pertain between different classes of cladistic information was undertaken. A general class of information, n-taxon statements, is recognized as a form of cladistic information in terms of which triplets (threetaxon statements), components, and subset nestings can be described. Disqualifiers (the negations of n-taxon statements) comprise an additional class of cladistic information. As is widely recognized, strict and Adams consensus methods have problems of insensitivity and ambiguity, respectively. New consensus methods were developed that solve these problems. The reduced Adams consensus method was developed to facilitate the unambiguous interpretation of Adams consensus trees. The reduced cladistic consensus method provides a solution to the problem of graphically representing all n-taxon statements that are common to a set of fundamental trees. A means of representing common disqualifiers using disqualifier-faithful subtrees is also suggested. The utility of consensus methods is discussed in the light of the development of the new methods, including the use of consensus trees in the measure of support and in supportbased randomization tests.