Repeating patterns represent temporal relations among data items, which could be used for data summarization and data prediction. More and more data of various applications is generated as a data stream. Based on time sensitive concern, mining repeating patterns from the whole history data sequence of a data stream does not extract the current trend of patterns over the stream. Therefore, the traditional strategies for mining repeating patterns on static database are not applicable to data streams. For this reason, an algorithm, named appearing-bit-sequence-based incremental mining algorithm, for efficiently discovering recently repeating patterns over a data stream is proposed in this paper. The appearing bit sequences are used to monitor the occurrences of patterns within a sliding window. Two versions of algorithms are proposed by maintaining the appearing bit sequences of maximum repeating patterns and closed repeating patterns, respectively. Accordingly, the cost of re-mining repeating patterns over a sliding window is reduced to that of monitoring frequency changes of the maintained patterns. The experimental results show that the incremental mining methods perform much better than the re-miming approach.