Abstract: On 7 September 2012, two earthquakes took place consecutively at the boundary between Yiliang county in Yunnan Province and Weining county in Guizhou Province, southwestern China. They are characterized by a short time-interval, close epicentral position and small difference in the earthquake magnitude, which provides a number of valuable strong ground motion recordings for analyses and researches on random characteristics of ground motions. In the present paper, the correlative characteristics of seismic stochastic process through correlation functions of acceleration histories are studied from the aspect of the set systems and sample functions. The results show that, correlation matrices of set systems for ground motions during the two earthquakes are random. Comparison with autocorrelation matrices indicates that cross-correlation matrices show greater randomness. Set systems that are composed of acceleration histories for the two earthquakes with the same station are correlated better than those for individual earthquake. Correlation functions of sample functions both show irregular fluctuant attenuation characteristics; correlation of sample functions becomes poorer with time difference of the sampling values increasing. In comparison with great earthquake (such as the Chi-Chi earthquake), correlation matrices and autocorrelation functions after decomposition of the moderate ground motion recordings both exhibit different characteristics. Because both two earthquakes have smaller ground motion amplitudes and weaker soil nonlinear effect, so the results provide new references for understanding the random characteristics of ground motions.