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Problems of application of nonparametric goodness-of-fit tests and x/sup 2/ type tests have been considered. The following points concerning the tests of x/sup 2/ type have been considered: (a) correctness problems in usage of x/sup 2//sub k-r-1/ -distributions as the limiting distribution laws depending on estimation method used; (b) grouping methods providing maximal test power for close alternative hypotheses; (c) choice of the optimal interval number by the maximal test power. Optimal grouping tables have been constructed. Nonparametric tests of Kolmogorov type, /spl omega//sup 2/ and /spl Omega//sup 2/ Mises type lose their property of "independence from distribution" in composite hypothesis testing. The limiting distribution laws depend on the distribution corresponding to the hypothesis under test, number and type of estimated parameters, their values and the estimation method. The models of limiting distributions for nonparametric test statistics have been constructed for a number of composite hypotheses. Obtained results are included in the GOSSTANDART recommendations of Russia "Applied statistics. Rules of check of experimental and theoretical distribution of the consent". Part 1 Goodness-of-fit tests of a type chi-square (P 50.1.033-2001), part 2 Nonparametric goodness-of-fit tests (P 50.1.037-2002).