Abstract: Firstly,based on the theory of runs distribution in one-dimensional random process,the theory of run distributions in multi-dimensional random processes is presented in this paper.Here,random processes are classified in four types:(1) Processes are independent on spatial and temporal scales; (2) Processes are independent on spatial scale and correlated on temporal scale; (3) Processes are corre-lated on spatial scale and independent on temporal scale; (4) Processes are correlated bot hon spatial and temporal scales.Secondly,the statistic method is used to test the accuraucy of developed runs theory.Finally the results from the application of runs theory to Yellow River historial droughtevents reappear characters show that return period of annual drought event taking place in middle reach and lower reach of the Yellow River at the same time is 5.78 years,return period exceeding one year is 7.76 years,and exceeding three years is 110 years etc.