AbstractIt is argued that both the principle of parsimony and the theory of evolution, especially that of natural selection, are essential analytical tools in phylogenetic systematics, whereas the widely used outgroup analysis is completely useless and may even be misleading.In any systematic analysis, two types of patterns of characters and character states must be discriminated which are referred to as completely and incompletely resolved. In the former, all known species are presented in which the characters and their states studied occur, whereas in the latter this is not the case.Dependent on its structure, a pattern of characters and their states may be explained by either a unique or byvariousconflicting, equally most parsimonious hypotheses of relationships. The so‐called permutation method is introduced which facilitates finding the conflicting, equally most parsimonious hypotheses of relationships. The utility of the principle of parsimony is limited by the uncertainty as to whether its application in systematics must refer to the minimum number of steps needed to explain a pattern of characterts and their states most parsimoniously or to the minimum number of evolutionary events assumed to have caused these steps. Although these numbers may differ, the former is usually preferred for simplicity.The types of outgroup analysis are shown to exist which are termed parsimony analysis based ontest samplesand cladistic type of outgroup analysis. Essentially, the former is used for analysing incompletely resolved patterns of characters and their states, the latter for analysing completely resolved ones. Both types are shown to be completely useless for rejecting even one of various conflicting, equally most parsimonious hypotheses of relationships.According to contemporary knowledge, this task can be accomplished only by employing the theory of evolution (including the theory of natural selection). But even then, many phylogenetic‐systematic problems will remain unsolved. In such cases, arbitrary algorithms like those offered by phenetics can at best offer pseudosolutions to open problems.Despite its limitations, phylogenetic systematics is superior to any kind of aphylogenetic systematics (transformed cladistics included) in approaching a (not: the) “general reference system” of or