Testing hypothesis versus nonparametric alternatives

We point out necessary and sufficient conditions of uniform consistency of nonparametric sets of alternatives approaching with hypothesis for widespread nonparametric tests. Nonparametric sets of alternatives can be defined both in terms of distribution function and in terms of density (or signals in the problem of signal detection in Gaussian white noise). Such conditions are provided for $\chi^2-$tests with increasing number of cells, Kolmogorov test, Cramer-von Mises tests, tests generated $\mathbb{L}_2$- norms of kernel estimators and tests generated quadratic forms of estimators of Fourier coefficients. Necessary and sufficient conditions of existence of consistent tests are explored as well.