Keywords : temporal processing, temporal extraction, tense, aspect, hybrid approaches, deep linguistic processing, shallow linguistic processing The full-fledged processing of temporal information presents specific challenges. These difficulties largely stem from the fact that the temporal meaning conveyed by grammatical means interacts with many extra-linguistic factors (world knowledge, causality, calendar systems, reasoning). This article proposes a novel approach to this problem, based on a hybrid strategy that explores the complementarity of the symbolic and probabilistic methods. A specialized temporal extraction system is combined with a deep linguistic processing grammar. The temporal extraction system extracts eventualities, times and dates mentioned in text, and also temporal relations between them, in line with the tasks of the recent TempEval challenges; and uses machine learning techniques to draw from different sources of information (grammatical and extra-grammatical) even if it is not explicitly known how these combine to produce the final temporal meaning being expressed. In turn, the deep computational grammar delivers richer truth-conditional meaning representations of input sentences, which include a principled representation of temporal information, on which higher level tasks, including reasoning, can be based. These deep semantic representations are extended and improved according to the output of the aforementioned temporal extraction module. The prototype implemented shows performance results that increase the quality of the temporal meaning representations and are better than the performance of each of the two components in isolation.