This paper reports on laser surface remelting experiments performed on a Zn-2wt.%Cu hypoperitectic alloy by employing a 5kW CW CO2 laser at scanning velocities between 6 and 1207mm/s. The growth velocities of the microstructures in the laser molten pool were accurately measured. The planar interface structure caused by the high velocity absolute stability was achieved at a growth velocity of 210 mm/s. An implicit expression of the critical solidification velocity for the cellular-planar transition was carried out by nonlinear stability analyses of the planar interface.The results showed a better agreement with the measured critical velocity than that predicted by M-S theory. Cell-free structures were observed throughout the whole molten pool at a scanning velocity of 652 mm/s and the calculated minimum temperature gradient in this molten pool was very close to the critical temperature gradient for high gradient absolute stability (HGAS) of the η phase. This indicates that HGAS was successfully achieved in the present experiments.