In this research Multifractal Indicators Evolution is considered. The Idea of this research is to provide approach that is able to indicate complicated changes in multifractal spectrums of World Stock Indexes. This approach should be able to x market instability to signi cant subsidence. This approach should be bene cial for the most European and Asia stock indexes forecasting and simulations. Financial market is a complex system, which requires a deeper and comprehensive understanding of nancial risks. Needs new risk measurement approaches and methods. For many years economists, statisticians, and stock market players have been interested in developing and testing models of stock price behavior. Since Stock Index Multifractal Scaling Exponent spectrum is found using Wavelet Transform Modulus Maxima (WTMM) approach (for Skeleton function estimation) and standard Multi- fractal Formalism procedure is completed ( rst Fractal Partition Function is constructed, then Moment Generating Function is calculated, after that Local Scaling Exponents Spectrum is esti- mated, than Multifractal Spectrum is approximated with quadratic function), Continuous Wavelet transform procedure is applied for Multifractal Spectrum approximation polynomial coecients, that are analysed in time space. In this article most European and Asia stock indexes are considered. Objects of experiment are 9 worldwide stock indexes: Dow Jones Industrial Average, AEX, CAC40, DAX30, IBEX, FTSE100, Nikkei225, SMI, STI. The Dow Jones Industrial Average index is considered for the whole available period: from 01/01/1900 to 01/04/2012, other mentioned indexes were analyzed during the following period: 05/07/1993 to 01/04/2012. In this research World Stock Indexes multifractal nature is analysed.