This paper presents and evaluates a two-level web usage prediction technique, consisting of a neural network in the first level and contextual component predictors in the second level. We used Markov chains of different orders as contextual predictors to anticipate the next web access based on specific web access history. The role of the neural network is to decide, based on previous behaviour, whose predictor’s output to use. The predicted web resources are then prefetched into the cache of the browser. In this way, we considerably increase the hit rate of the web browser, which shortens the load times. We have determined the optimal configuration of the proposed hybrid predictor on a real dataset and compared it with other existing web prefetching techniques in terms of prediction accuracy. The best configuration of the proposed neural hybrid method provides an average web access prediction accuracy of 86.95%.