Rise of non-classical science during XX century had certain influence upon development of biological taxonomy. Scientific pluralism (especially normative naturalism of Laudan), contrary to positivist and early post-positivist treatments, made taxonomy acknowledged scientific discipline of its own right. The present state of some schools of taxonomy makes it possible to consider them as a part of non-classical science and constituting the non-classical taxonomy. The latter is characterized by the following most important features. Ontological substantiation of both classificatory approaches and particular classifications is requested which invalidates such formal approaches as nominalistic and phenetic (numerical) schools. This substantiation takes a form of content-wise background preferably causal models which include certain axioms and presumptions about taxonomic diversity being studied, together with its causes, and thus define initial conditions of classificatory procedures. From this viewoint, phylogenetic classificatory approach is the most developed part of non-classical taxonomy. The entire taxonomic diversity is structured into several aspects of different levels of generality, each being outlined by a particular consideration aspect. The latter makes personal knowledge constituting an irremovable part of any scientific statement about taxonomic diversity, thus opposition of "objectively" and "subjectively" elaborated classifications becomes vague. Interrelation of various species concepts corresponding to its different consideration aspects is described by uncertainty relation principle. Classificatory algorithms are to be compatible with the conditions of a background model to ensure particular classifications obtained by their means are interpretable within the same model: this is provided by the correspondence principle. Classification is considered as a taxonomic hypothesis, i.e. a conjectural judgement about structure of particular fragment of taxonomic diversity considered within given consideration aspect; wich is to be forwarded and tested according to certain rules. Recognition of different aspects of taxonomic diversity makes it "legal" to elaborate several classifications of equal status, each reflecting a particular aspect of a fixed fragment of that diversity. This viewpoint makes classical ideas of the "ultimate" Natural (whatever might be its definition) or the best reference systems futile. In general, any pretension of an approach to be "the best" in reflecting taxonomic divesrity is contr-productive. Instead, elaboration of particular spectra of complementary classifications becomes the main task of non-classical taxonomy which describes in sum the entire taxonomic diversity. So, not opposition but correct mutual interpretation of such classifications and uniting them into the comprehensive picture of taxonomic diversity become focal points of non-classical taxonomy.