With the decrease of global temperature, glacial epoch came over the earth and global climate fluctuated over a great range since the beginning of Quaternary. Paleoclimotologists of various countries have focussed attention to the periodic characteristics and dynamics of climatic fluctuation in the past many years (Berger, 1977; Imbrie and Hays, 1984; Ding Zhongli et al., 1990; Yu Zhiwei et al., 1992; Liu Youmei et al., 1996). Although some of the workers have paid their attention to the nonlinear characteristics of the global Quaternary environmental evolution (Nicolis and Nicolis, 1984; Lu Houyuan et al., 1993), it is worth while to do this kind of work in some special areas in the world, for example the Qinghai|Tibet Plateau.; Using R/S analysis, the authors calculated the Hurst indexes H of some geochemical proxies, including organic carbon, FeO, Fe-2O-3 and FeO/ Fe-2O-3, from the Tianshuihai Lake core in West Kunlun Mountain of the Qinghai|Tibet Plateau. The proxies satisfy the Hurst law with H-{org.carbon}=0.735, H-{Fe-2O-3}=0.757, H-{FeO}=0.848 and H-{FeO/Fe-2O-3}=0.646. All the indexes are greater than 0.5, meaning that from 240 to 15 ka B.P., there were some long|run dependencies|persistence in the climatic and environmental evolution around the Tianshuihai Lake area. This is in accordance with the climate there from 240 to 15 ka B.P. (Yu Suhua et al., 1996). The paleo|climate and paleo|environment evolution around the Tianshuihai Lake area is of persistence as well as of fluctuation and is a combination of these two components. There are some differences between the four Hurst indexes, which probably resulted from the different intensities of persistence of the four proxies, organic carbon, FeO, Fe-2O-3 and FeO/ Fe-2O-3, or from the change of drainage system around the Tianshuihai Lake area from openness to closeness(Li Bingyuan et al., 1991; Sun Honglie, 1996; Shi Yafeng et al., 1998).; The Qinghai|Tibet plateau was the starter and sensor of the climatic and environmental variation of the surrounding areas (Yao Tandong et al., 1991; Feng Song et al., 1998) and some other scientists even regarded it as the driver and amplifier of global climatic variations (Pan Baotian and Li Jijun, 1996). The persistence in which the climate and environment around the Tianshuihai Lake area evolved from 240 to 15 ka B.P. is probably a function of the continuous uplift of the plateau in the same period of time. With the decrease of global temperature, glacial epoch came over the earth and global climate fluctuated over a great range since the beginning of Quaternary. Paleoclimotologists of various countries have focussed attention to the periodic characteristics and dynamics of climatic fluctuation in the past many years (Berger 1977; Imbrie and Hays, 1984; Ding Zhongli et al., 1990; Yu Zhiwei et al., 1992; Liu Youmei et al., 1996). Although some of the workers have paid their attention to the nonlinear characteristics of the global Quaternary environmental evolution (Nicolis and Nicolis, 1984; Lu Houyuan et al., 1993), it is worth while to do this kind of work in some special areas in the world, for example the Qinghai | Tibet Plateau. ; Using R / S analysis, the authors calculated the Hurst indexes H of some geochemical proxies, including organic carbon, FeO, Fe - 2O - 3 and FeO / Fe - 2O - 3 from the Tianshuihai Lake core in West Kunlun Mountain of the Qinghai | Tibet Plateau. The pro xies satisfy the Hurst law with H - {org.carbon } = 0.735, H - {Fe - 2O - 3 } = 0.757, H - {FeO } = 0.848 and H - {FeO / Fe - 2O - 3 } = 0.646. All the indexes are greater than 0.5, meaning that from 240 to 15 ka BP, there were some long | run dependencies | persistence in the climatic and environmental evolution around the Tianshuihai Lake area. This is in accordance with the climate there from 240 to 15 ka BP (Yu Suhua et al., 1996). The paleo climate and paleo | environment evolution around the Tianshuihai Lake area is of persistence as well as of fluctuation and is a combination of these two components. There are some differences between the four Hurst indexes, which probably assume from the different intensities of persistence of the four proxies, organic carbon, FeO, Fe - 2O - 3 and FeO / Fe - 2O - 3, or from the change of drainage system around the Tianshuihai Lake area from openness to closeness (Li Bingyuan et al., 1991; Sun Honglie, 1996; Shi Yafeng et al., 1998)The Qinghai | Tibet plateau was the starter and sensor of the climatic and environmental variation of the surrounding areas (Yao Tandong et al., 1991; Feng Song et al., 1998) and some other scientists even thought it as the driver and amplifier of global climatic variations (Pan Baotian and Li Jijun, 1996). The persistence in which the climate and environment around the Tianshuihai Lake area evolved from 240 to 15 ka BP is probably a function of the continuous uplift of the plateau in the same period of time.