The periodical nonlinear behavior of a number of sequences of radiative Cepheid models is computed and Fourier analyzed. The Fourier phases and amplitudes exhibit systematic and characteristic variations when plotted as a function of the period ratio P2/P0, but not as a function of the period or the effective temperature. The dominant role played by the 2:1 resonance between the fundamental mode and the second overtone is clearly established. The astrophysical consequences of the observed tightness of the Fourier phase phi(21) versus period relation are thoroughly discussed. It is demonstrated that the dispersion of phi(21) can be used to estimate the width of the instability strip, independently of the Cepheid temperature and luminosity calibrations. Comparison of such an estimation with the traditional determination of that width provides a new test for pulsation and evolution theories.