The response of the lamellar spacing to abrupt change of the solidifying rate for Al-Si eutectic during directional solidification has been investigated both experimentally and theoretically. When the solidifying rate was changed abruptly, the response of the lamellar spacing was gradual and retarded, which was attributed to the "cluster branching" and "cluster terminating" mechanisms of the lamellar phases. The retarded distance, as a function of the abrupt change factor, rho, for both rho > 1 and rho < 1, has been evaluated, and the uniqueness of the spacing selection has been verified. A theoretical approach of the response dynamics has been presented by considering the solute diffusion in liquid and the growth anisotropy effect of the eutectic lamella. A dynamic factor has been introduced to characterize the growth anisotropy. Excellent agreement between the theoretical approach and the measured results has been shown. Finally, this theory has been successfully applied to describe non-steady-state directional solidification of Al-Si eutectic with constant accelerating solidification rate.