The problem of evaluation and the analysis of distribution of power is consi­dered in the State Duma of the Russian Federation for 1994-2003. Banzhaf power index is used to evaluate the power of fractions and groups in the Russian Parlia­ment for the simple and constitutional majority decision making and under different assumptions about admissible coalitions. It is analyzed how the index is changed un­der different changes in structure of fractions and groups and under different sce­narios of coalition formation. The dependence in the changes of index values is com­pared with respect to political events during this period.