The article presents a proposal, design and implementation of a new approach to adaptive e-learning systems. First, a proposal of a model is presented. This model aims at introducing adaptivity to current e-learning systems, which are rigid and limited in offering a truly personalised learning to individual students. Many of current e-learning systems enable personalised learning. However, in this paper, there is a new, innovative approach proposed for an adaptive personalised e-learning system. The primary area of our research is English as a second language (ESL). Adaptivity in our view is considered as an ability of the system to adapt to student's knowledge and characteristics. This pedagogical perspective requires introduction of such processes that enable to work the pedagogical aspects of teaching/learning. The required processes are of informatics nature. The proposed model was subsequently designed into a real application. Finally, the application was implemented and verified on a real data set. The results are also provided. (C) 2017 Elsevier Ltd. All rights reserved.