In fluorescence analysis,the phenomenon of overlapping often occurs among adjacent peaks.In the view of the random physical properties of formation process of X fluorescence spectra,Gaussian Mixture Statistics Model (GMSM) and Genetic Algorithms were used for the decomposition of overlapping peaks.First,the GMSM was proposed to describe the overlapping peaks,and the local convergence problem of expectation maximization (EM) was analyzed.Secondly,the GMSM parameters were regarded as individual genes,and the log-likelihood function of overlapping peaks random data was set as fitness function.A fast algorithm for the objective function value was proposed.Finally,the population search technology of Genetic Algorithm was used to find the global optimal solution,and to realize the decomposition of overlapping peaks.All measured data were regarded as “useful” data.The “useful” degree was reflected by their probability.The GMSM method can achieve the “best match” effect in the maximum global probability with zero loss of original data,which can fit the random of radiation measurement process.The decomposition experiments of four serious overlapping peaks show high precision of the peak position,peak area and standard deviation.The maximum error was 0.7 channel,2.3% and 2.17%,respectively,which is especially suitable for the condition of serious overlap and can be widely used for the decomposition of other energy spectrum.