In the last two decades, rapid range expansions of the invasive Ponto-Caspian round goby (Neogobius melanostomus) have been reported from many large waterbodies in Europe and North America. A high invasion potential of this species has been reported through its opportunistic life-history traits and high phenotypic plasticity. Nevertheless, it appears that unlike many other invasive fish species, N. melanostomus has not been able to colonize small and mid-size tributaries of large rivers (streams of order higher than two or three). Given that the invasion history of N. melanostomus in Europe is still rather short, and its invasion potential so high, its future possible expansion represents a big question with important ecological, conservation and management implications. One of the ways to answer this question is to identify the key environmental parameters important for further expansion of N. melanostomus, and to compare these with other successful invaders with longer histories, e.g. topmouth gudgeon (Pseudorasbora parva) and pumpkinseed (Lepomis gibbosus). In this study, basic environmental, physicochemical and chemical parameters, biological elements and human disturbances in all types of streams in Slovakia were analysed in order to identify the key factors that discriminate habitats where the three invasive species were present relative to those where they were not. Random Forest Analysis was used to predict and assess the relationship among the large number of potential predictor variables and a dependent variable. This method is useful especially when large numbers of correlated predictors are evaluated and both quantitative and qualitative predictors are involved. The main aim of this study was to estimate potential for further spread of the three invasive species, with an emphasis on the possibility of further expansion of N. melanostomus into small and mid-size tributaries of large rivers. The habitat parameters that characterize current distribution limits of N. melanostomus were found to be the wetted width, slope, pH, temperature and conductivity. The species was found to prefer wider wetted width and shallower slope, higher oxygen saturation and slightly alkaline pH. Nevertheless, the altitude (often considered a surrogate of several habitat parameters) limits current distribution of N. melanostomus both in Slovakia and other regions of Europe. Thus, in contrast to other successful invaders (L. gibbosus and P. parva) the analysis of key factors regulating current distributions of N. melanostomus suggests that its future spread into small and mid-size tributaries of large rivers is unlikely.