We describe in detail how ZnO films grow on In0.53Ga0.47As substrates by Atomic Layer Deposition (ALD), employing a suite of in situ synchrotron X-ray techniques. Combining results from different measurements allows the distinguishment of three different growth behaviors: an initial, slow linear growth, often referred to as a growth delay (regime I), followed by a nonlinear growth (regime II), and finally, a steady, linear growth (regime III), the last of which is the self-limited growth behavior characteristic of ALD. By the end of the regime I, the In0.53Ga0.47As surface is covered with an ultra-thin, poorly-ordered Zn oxide layer. The transition from regime I to II is clearly evidenced by the appearance on the X-ray absorption spectra of characteristic features of the wurtzite structure, as well as the nucleation and growth of ZnO grains (3D) on top of the poorlyordered Zn oxide layer. Regime II ends when the growth per cycle reaches a constant level. We show that the water pressure during growth has an impact on the duration of the growth delay (regime I), unlike the substrate temperature. In the regime of steady growth, we observe that the rate of deposition obtained for all temperatures inside the ALD window is 0.17 nm.cy −1. The deposition temperature has clear effects on the film texture and initial crystallization behavior, as well as the final crystallinity and thicknesses of the layers adjacent to the In0.53Ga0.47As substrate. Based on the experimental results and earlier ab initio calculations and Monte Carlo simulations of ZnO ALD on ZnO, we suggest reaction mechanisms consistent with our findings and present a model of growth starting from the very earliest stages of deposition to the steady growth regime.