The South Asian high (SAH) in summer is a strong anticyclone over the Tibetan Plateau and adjacent areas. It is an important component of the Asian summer monsoon. The east-west oscillation of the SAH is an important characteristic and is closely related to the weather situation and climate change of Asia-especially the distribution of drought and flood. It is found that the east-west oscillation of the SAH is not only manifested as the zonal expansion of the area,but also the adjustment of different forms. The climatological mean center position of the SAH is usually located over the Tibetan Plateau,a nd the SAH has multiple centers in general. The different centers often appear over the Iranian Plateau, the Tibetan Plateau,eastern China,or the western Pacific. The SAH can be classified into different forms according to the number and location of these SAH centers. Identifying the circulation features and maintenance mechanisms of the different forms can help research the mechanism of the eastwest oscillation of the SAH. In this paper,based on NCEP-NCAR monthly mean height and wind field reanalysis data from 1948 to 2013, the SAH is classified into several forms according to its center numbers and center location using composite analysis. In addition, the relationship between the circulation characteristics of different SAH forms and the atmospheric circulation in the Northern Hemisphere is discussed. The results obtained are as follows: (1) The SAH can have between one and five centers,among which having two or three centers constitutes the majority,accounting for 82% of the total samples. Next, is the SAH with a single center,accounting for 14% of the total samples,and the remainder comprises SAHs with four or five centers,accounting only for 3% of the total samples. (2) The SAH can be classified into different forms according to the number of centers, the meridional position and the circulation features. SAHs with only one center can be classified into Ⅰ1 form and I2 form,accounting for 44% and 56% of the total samples, respectively. SAHs with two centers can be classified into Ⅱ1 form, Ⅱ2 form and Ⅱ3 form,accounting for 66.7%, 18.5% and 14.8% of the total samples, respectively. Ⅲ1 form is the only form with three centers considered,accounting for 67% of the total samples. (3) The center of Ⅰ1 form SAHs is located over the Iranian Plateau,and the center of Ⅰ2 form SAHs is located over the Tibetan Plateau. The two centers of Ⅱ1 form SAHs are located over the Iranian Plateau and Tibetan Plateau, respectively. The centers of Ⅱ2 form SAHs are located over the Iranian Plateau and western Pacificeastern China, respectively. The two centers of Ⅱ3 form SAHs are located over the Tibetan Plateau and western Pacific-eastern China, respectively. The three centers of Ⅲ1 form SAHs are located over the Iranian Plateau, the Tibetan Plateau and western Pacific-eastern China, respectively. (4) The geopotential height fields and temperature fields in the upper-middle troposphere feature significant positive anomalies in those areas where the SAH is located,and the maintenance mechanisms of the temperature anomaly fields in different regions are also different. Therefore, the east-west oscillation of the SAH can also be expressed as the conversion of the different forms of the SAH,which is closely related to the temperature in the upper-middle troposphere. Moreover, the conversion of the different forms of the SAH affects the atmospheric circulation and the distribution of precipitation in Asia.