In this work we build two families of nonparametric tests using tapered data for the off-line detection of change-points in the spectral characteristics of a stationary Gaussian process. This is done using the Kolmogorov±Smirnov statistics based on integrated tapered periodograms. Convergence is obtained under the null hypothesis by means of a double indexed (frequency±time) process together with some extensions of Dirichlet and Fejer kernels. Consistency is proved using these statistics under the alternative. Then, using numerical simulations, we observe that the use of tapered data signicantly improves the properties of the test, especially in the case of small samples.