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Abstract: The local singularity model involved in the context of multifractal theory calculates an index which indicates the local elemental enrichment or depletion and can be used to delineate the weak anomalies. The index, called singularity exponent can be calculated using the total amount model and density model, respectively. The former is based on the power–law relationship between the cumulative concentrations of the neighboring samples in variable cell sizes and cell size, while the latter is between the average concentration and cell size. The influence of the two models on the calculation of the local singularity was estimated in this paper. The total amount model was thought to be preferable in calculating the singularity exponent, which was applied to stream sediment data from the Xiong''ershan gold and molybdenum ore district, Western Henan province, China, and an algorithm based on the window-based method was advanced to map the local singularity distributions of Au and Mo. The thresholds of Au and Mo calculated on the singularity map were used to delineate anomalies which were associated not only with known gold and molybdenum ore deposits in the northern part of EW-trending Machaoying fault, but also with the areas south of Machaoying fault where no gold deposits have yet been discovered. Neither were they clearly identified by the Concentration–Area model and mean+standard deviation of Au concentrations. The results show that weak anomalies hidden within the strong variance of background can be well identified by the local singularity model, and the delineated anomalies should be considered as favorable target areas. [Copyright &y& Elsevier]