The present article stipulates on various disputable issues of applying the general legal maxims on overcoming the conflict of lex posterior derogate priori and lex specialis derogate legi generali based on the empirical examples of contemporary Russian criminal law. The objective is to clear the peculiarities of operating the lex posterior and lex specialis maxims including, inter alia, through appealing to the doctrine and positive law in the aspect of correlation with some specific colnflict rules. For this purpose, the author turns to a number of techniques, ways and methods of legal phenomena studies, such as, particularly, system approach, ascend from abstract to specific, using the logic of standard and normative statements, conceptual and definition analysis, speculative experiment, legal and dogmatic approach, legal simulation method, law comparison method. The main conclusion of the research is formulated as follows: though the principles of lex specialis and lex posterior are generated by the legal doctrine as criteria for selecting one out of two conflicting options, the principle that a law governing a specific subject matter overrides a law governing only general matters finds a wider scope of application compared to the principle of priority of a new law over the old one. The situation is explained by the fact that lex specialis is deliberately used by the legislators to construct logical relationships of legal rules, while lex posterior does not perform a similar function