Periodic spectral characteristics of earthquake activity in the seismic strengthening areas of 24 ewthquakes withM≥ 6.0 are studied by the maximum entropy spectral method whose superiority is tested. Then the follow resultshave been obtained : ① The periodic spectra of seismic activity in seismic strengthening areas are different indifferent stage in earthquake-generating processes. Long periodic spectra and short ones coexist in normal stage,while only short ones (on average, 43% of long ones) exist and long ones disappear prior to ear’thquakes. ② Theappearing time of short period before earthquakes has some relations with magnitude. The result shows thatdecades or even one hundred years is the common value for a great earthquake of M=8.0, 30 years for one withmagnitude about 7 and 20-30 years for a strong quake of M=6.0. For the same magnitude earthquakes in differentregions the appearing time is also different. For example, it is longer in North China than that in the western pan ofChina. Then the characteristics are preliminarily explained applying the strong body earthquake-generating model.Applying the maximum entropy spectral method, the idea of tendency prediction for strong and great earthquakesis suggested and used into practice. for example. the tendency predictions of the Wuding earthquake with M=6.5and the Lijiang earthquake of M=7.0 in Yunnan Province got some positive effects. So a new method of tendencyprediction of M≥6.0 earthquakes is offered. Periodic spectral characteristics of earthquake activity in the seismic strengthening areas of 24 ewthquakes with M ≥ 6.0 are studied by the maximum entropy spectral method whose superiority is tested. Then the follow results have been obtained: ① The periodic spectra of seismic activity in Long periodic spectra and short ones coexist in normal stage, while only short ones (on average, 43% of long ones) exist and long ones disappear prior to ear’thquakes. ② Theappearing time of short period before earthquakes has some relations with magnitude. The result shows that deccades or even one hundred years is the common value for a great earthquake of M = 8.0, 30 years for one with magnitude about 7 and 20-30 years for a strong quake of M = 6.0 For the same magnitude earthquakes in differentregions the appearing time is also different. For example, it is longer in North China than that in the western pan of China. Then the characteristics are preliminarily explained applying the strong body earthquake-generating model. Applying the maximum entropy spectral method, the idea of ​​tendency prediction for strong and great earthquakesis suggested and used into practice. for example. the tendency predictions of the Wuding earthquake with M = 6.5 and the Lijiang earthquake of M = 7.0 in Yunnan Province got some positive effects. So a new method of tendency prediction of M≥6.0 earthquakes is offered.