This paper examines the uncertainty events encountered in the process of constructing highways, and evaluates their impact on construction time, on highway projects in South Africa. The rationale for this examination stems from the view held by scholars that the construction of highways is a complex process, taking place in changing environments and often beset by uncertainties; and that there is a lack of appropriate evaluation of these uncertainty events occurring during the construction process. The research made use of a review of extant literature in the area of uncertainty management, and modeling in infrastructure projects, to guide the direction of the study. The inquiry process consisted of brainstorming by highway experts and interviewing them to identify the uncertainty factors that impact construction time. An uncertainty matrix for South African highway projects was developed, using a quantitative model and descriptive statistics. It emerged from the study that the uncertainty events affecting the construction time of highway projects are distributed across economic, environmental, financial, legal, political, social and technical factors. Also, it was found that each factor might account for several uncertainty events which impact on construction time differently, through a combination of the uncertainty events of the individual construction activities. Based on the obtained data, an Adaptive Neuro Fuzzy Inference System (ANFIS) has been developed, as a simple, reliable and accurate advanced machine learning technique to assess the impact of uncertainty events on the completion time of highway construction projects. To validate the ANFIS model, the Stepwise Regression (SR) models have been designed and their results are compared with the results of the ANFIS. Based on the predicted impact size of uncertainty events on the time of highway projects, it can be concluded that construction time on South African highway projects is significantly related to the social and technical uncertainties factors.