Abstract: Time series have been widely used in many fields of nature and society. And they can be divided into single time series and multiple time series. Multiple time series, consisting of interrelated single time series, can describe an object by many aspects. Therefore, multiple time series are more complex than single time series. At present the research of time series mainly focuses on single time series, and the research of multiple time series is relatively little, such as the query over multiple time series. However, multiple time series are very useful in our life. In addition, most of researches of single time series cannot be used in or extended to multiple time series directly, which makes the study of multiple time series necessary. In this paper we give the definition of the dominant relation between multiple time series, and then propose the k'/k-dominant skyline query over multiple time series. We also present the proof of correctness of algorithms in this paper. Finally a set of experiments are conducted on both synthetic and real data to verify the proposed algorithms. The experiment results prove that both of these two algorithms are effective, and GMI algorithm is much more efficient than GMS.