Outlier detection has become an increasing challenging data-mining task in modern applications due to the fact that the data may come in the form of streams rather than batches. In this thesis, we will present two online algorithms to detect outliers over data streams, based on the sliding window approach, to address all the challenges when processing data over streams. Both algorithms keep statistical summaries of previous windowed data in memory that help with the decisions of future data and do not require a secondary memory. Proved by different datasets, our proposed methods can detect outliers accurately over data streams, where data distribution may change over time.