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Mining frequent episodes aims at recovering sequential patterns from temporal data sequences, which can then be used to predict the occurrence of related events in advance. On the other hand, gradual patterns that capture co-variation of complex attributes in the form of " when X increases/decreases, Y increases/decreases" play an important role in many real world applications where huge volumes of complex numerical data must be handled. Recently, these patterns have received attention from the data mining community exploring temporal data who proposed methods to automatically extract gradual patterns from temporal data. However, to the best of our knowledge, no method has been proposed to extract gradual patterns that regularly appear at identical time intervals in many sequences of temporal data, despite the fact that such patterns may add knowledge to certain applications, such as e-commerce. In this paper, we propose to extract co-variations of periodically repeating attributes from the sequences of temporal data that we call seasonal gradual patterns. For this purpose, we formulate the task of mining seasonal gradual patterns as the problem of mining periodic patterns in multiple sequences and then we exploit periodic pattern mining algorithms to extract seasonal gradual patterns. We discuss specific features of these patterns and propose an approach for their extraction based on mining periodic frequent patterns common to multiple sequences. We also propose a new anti-monotonous support definition associated to these seasonal gradual patterns. The illustrative results obtained from some real world data sets show that the proposed approach is efficient and that it can extract small sets of patterns by filtering numerous nonseasonal patterns to identify the seasonal ones.