Applicability of the Bloch equations for describing relaxation in the saturation regime is studied experimentally and theoretically. Hole burning in the proton NMR line of water was observed, and the shape and width of the hole were investigated in a well-characterized noise field. The behavior of power broadening is remarkably different from that expected from the Bloch equations and strongly depends on the correlation time of the noise field. The hole shape is not a single Lorentzian. The experimental results are well explained by a stochastic theory of power broadening. We show that the hole burning in well-characterized noise fields is very useful for the experimental test of power-broadening theories.