[en] A general review of the pulsating δ Scuti variables is given including the observed light curves and positions of the stars in the Hertzsprung-Russell diagram. Theoretical interpretations from evolution and pulsation calculations give their masses, radii, luminosities, and even their approximate internal compositions. Three models of these stars are discussed and used to study the nonlinear hydrodynamic behavior of these stars. The hydrodynamic equations and the Stellingwerf method for obtaining strictly periodic solutions are outlined. Problems of allowing for time-dependent convection and its great sensitivity to temperature and density are presented. Tentative results to date do not show any tendency for amplitudes to grow to large unobserved amplitudes, in disagreement with an earlier suggestion by Stellingwerf. It is found that the very small growth rates of the pulsations may even be too small to be useful in seeking a periodic solution. 15 refs., 8 figs., 3 tabs