Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Transient directional solidification experiments have been carried out with Zn-Mg hypoeutectic alloys under an extensive range of cooling rates with a view to analyzing the evolution of microstructure. It is shown that the microstructure is formed by a Zn-rich matrix of different morphologies and competitive eutectic mixtures (Zn-Zn11Mg2 and Zn-Zn2Mg). For 0.3 wt-pct Mg and 0.5 wt-pct Mg alloys, the Zn-rich matrix is shown to be characterized by high-cooling rates plate-like cells (cooling rates > 9.5 and 24 K/s, respectively), followed by a granular-dendritic morphological transition for lower cooling rates. In contrast, a directionally solidified Zn1.2 wt-pct Mg alloy casting is shown to have the Zn-rich matrix formed only by dendritic equiaxed grains. Experimental growth laws are proposed relating the plate-like cellular interphase, the secondary dendritic arm spacing, and the eutectic interphase spacings to solidification thermal parameters, i.e., cooling rate and growth rate. The experimental law for the growth of secondary dendritic spacings under unsteady-state solidifications is also shown to encompass results of hypoeutectic Zn-Mg alloys subjected to steady-state Bridgman growth.47A630523064FAPESP-Sao Paulo Research Foundation, Brazil [2012/08494-0, 2013/15478-3, 2013/25452-1, 2013/23396-7, 2014/50502-5]CNPq-The Brazilian Research CouncilCSIC-Spanish National Research Council [i-link0944]Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)