Abstract: In practice trace impurity is added to the eutectic melt to modify the solidified structures. Experiments on unsteady-state growth of irregular eutectic containing trace impurity are of much importance. The authors have conducted experiments on unsteady-state constant acceleration growth(CAG)and constant-deceleration growth(CDG) of Al-Si eutectic containing 0,5% lanthanum under constrained condition. The experimental findings are as follows!(1) For both CAG and CDG, mterfibre radius R of the eutecticcan respond without marked delay to the varying growth rate V;however, interflake spacing of the eutectic has slow response to therate V, Deviating growth of the second arm of the primary α-dendritefor CAG has been observed.(2) The amount of the fibrelike eutectic or CAG increases with increasing growth rale; however, for CDG the amount decreases with decreasing growth rate. Marked effects of the acceleration and the initial growth rate on the growth have not been observed The Flake-Fibre transition and the Fibre-Flake transition are continuous in entirety. (3) Accumulation of lanthanum in liquid in front of the growing interface has been observed, and the concentration of lanthanum in front of interface of the fibrelike eutectic is higher.(4) Analysis on solute-diffusion field in liquid has been advanced. Anrimportant factor is introduced to describe the controlling of the eutectic silicon branching and termination stopping on the field. The experiments have been interpreted by the model.