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How to dynamicaly model a devolopment of e-government system Electronic government or the term of e-government aims to improve and increase the accessibility of information, transactions, and government services by using the information and communications technologies (ICT) including the computers, the Internet, automation equipment and mobile devices. The main aim is to provide and satisfy the population needs with the focus on improvement of the e-government area. The authors introduce the potential approach for defining the system as a dynamic system of development the area of e-government. The procedure for solving the dynamic model, described in the article, that uses contemporary mathematic methods of so-called ,,Differential Equations Theory” with delayed argument, can be successfully used for both modelling further specific economic relations and for economic models in general and also in various conditions.