The article is devoted to the theoretical issues of developing methodology for studying systemic relations presented implicitly in the text of the explanatory dictionary of the Spanish language «Diccionario de la lengua española», 23ª edición. The methodology of the research and the formal representation of these relations are based on the theory of lexicographic systems and the theory of semantic states by NAS Academician Dr. Volodymyr Shyrokov. Based on the results of the study, the formal models are constructed for system relations such as hyperchains / hypercycles, quasi-semantics and synonymy. Characteristics and types of systemic relations are given. Hyperchains are the chains of words related to each other by the relationship “hyperоnym-hyponym”, “part-whole”, “process-result”, etc. Quasi-semantics is a property of a word to adopt its meaning from the other one from which it was derived. Quasisemantics combines both the meaning of the main word and its affix. There were twenty five definition patterns revealed in the dictionary for quasisemantic words. Synonymy is a language phenomenon, the essence of which is that the two or more lexical units, being in a certain semantic state, are able to replace each other in certain contexts. The synonyms registered in the dictionary represent not only semantic, but also pragmatic characteristics (style, domain, geographic area). In particular, synonymic couples are the following: special-purpose word / general-purpose word, general-purpose word / special-purpose word, special-purpose word / special-purpose word, colloquial word / literary word, ethnolect / common word. The research results are proposed to be used for creating various linguistic software: text processing systems, semantic analyzers, virtual lexicographic laboratories, etc.