In this paper we report on the electrodeposition process from a highly acidic aqueous sulphate electrolyte and discuss the relationships between electrochemical kinetics and crystalline structure of the electrodeposits. The electrochemical kinetics were studied by voltammetric and potentiostatic methods, showing the peculiarities of the cathodic process of highly acidic baths, leading - under suitable plating conditions - to the removal of the Te excess which is typical for the ZnTe electrodeposition systems reported in the literature. Potential transient techniques and scanning electron microscopy (SEM) imaging were used to study the nucleation. They showed that the nucleation process is instantaneous. The crystalline structure of the deposits was studied by X-ray diffraction (XRD), revealing the possibility of growing directly cubic ZnTe films under suitable electrochemical conditions. A minor amount of Te can form at the surface as a result of etching by the electrodeposition bath. Structural data were complemented by X-ray photoelectron spectroscopy (XPS) analyses and compositional measurements by energy dispersive spectrometry (EDS).