The growth of ZnTe nanowires and ZnTe-CdTe nanowire heterostructures is studied by in situ transmission electron microscopy. We describe the shape and the change of shape of the solid gold nanoparticle during vapor-solid-solid growth. We show the balance between one monolayer and two monolayer steps, which characterizes the vapor-liquid-solid and vapor-solid-solid growth modes of ZnTe. We discuss the likely role of the mismatch strain and lattice coincidence between gold and ZnTe on the predominance of two monolayer steps during vapor-solid-solid growth and on the subsequent self-regulation of the step dynamics. Finally, the formation of an interface between CdTe and ZnTe is described.