Problem setting. Improvement of the domestic system of the sources of law being the important part of the legal system of Ukraine modernization is virtually impossible without working out of the logically consistent and not internally contradictory theoretical model of the source of law, revealing of the vertical and horizontal ties between different sources of law, tendencies of their development, peculiarities of their interaction with other elements of the legal system. In connection with this it is actual and useful the investigation of the foreign models of the sources of law, regularities of their development and also implementation in the national legal system of the corresponding foreign legal experience. System analysis of sources of the Anglo-American of law gives the possibility to take a fresh look at such sources of law as normative-legal act and legal precedent, to reveal their shortcomings and advantages, peculiarities of their interrelation and interaction with secondary sources of law. Recent research and publications analysis. Works by W. Burnham, R. Cross, R. David, N. Duxbury, L. Fuller, J. Gray, J. Merryman, S. Pohrebniak, R. Pound, M. Radin, F. Schauer F. Shecaira, S. Shevchuk, K. Zweigert are noteworthy among modern scientists researching this problem. Paper objective. The main tasks and goals of the article set by the author are as follows: determination of the main approaches in the Anglo-American jurisdiction to the interpretation of the concept «source of law», determination of the interrelations and interaction between primary and secondary sources of law, peculiarities of their use in the legal practice , in particularly, in the case of enforcement of law. Paper main body. Complex historical process of the sources of law formation in the legal systems of the Anglo-American legal family has taken place under direct and significant influence of the judicial corps representatives. It is not only concerns of the main source of the Anglo-American law, that is, precedent being the product l of the court lawmaking. It is as the result of the activity of the judges that such sources of law as «general rules » of the courts, written by the prominent lawyers, mainly, by judges, so-called, «books of authority»; legal custom that acquire legal and regulatory character in the event of judicial sanctioning. Characterizing the role and significance of the legislation (statute law) in the legal life of the modern countries of the general law, determining its interrelations and interaction with the precedent law it is necessary to take into account that statute norms «revive» exactly in the court practice. The courts use the statute norms in the case when they have been interpreted by the highest judicial instances in the framework of the particular case decision. Conclusions of the research. The statement that enforcement of law is based on the formal and dogmatic approach to law and especially mechanical use of the legal regulations, in fact, making it impossible adoption of reasonable and equitable decisions is recognized among lawyers of the Anglo-American tradition. That is why, the judges in the countries of the Anglo-American law often turn to non-legal sources of law and secondary (additional) sources of law, first of all, to the scientific sources. Herewith, the legal science has influence on the enforcement of law in two basic forms. Firstly, when scientific statements become part of the legal consciousness of the enforcement of law subjects in the course of the study by them of the scientific works .In this case, we are talking about indirect influence of the scientific thought on the legally significant decisions made by judges . Secondly, under the conditions of the controversial practice of the norms of law use, presence of the gaps in the legislation, collisions of the legal regulations it is used by the judicial bodies scientific positions as mean of the additional argumentation referring in their decisions to lawyer authoritative works. This make their legal position more convincing, logical and well grounded.