This paper presents, for the first time, a systematic description of a new method of structural analysis of data, based on so-called monotonic systems. It is aimed at constructing a systematic description of the data. In this theory, the structure of the data is described as a sequence of mathematical objects - quasi-kernels, which gives this approach a certain resemblance to a classical agglomerative methods (however here the starting point of the sequence - the kernel - is determined by the theory). The paper mainly concerns itself with presenting the mathematical basis for the suggested methods. (pdf)