The formation and phase transitions of underpotentially deposited (√3×√3)R30° and (1×1) Cu adlayers on Au(111) were studied by in-situ STM. Upon a negative potential sweep from the region of a disordered lattice gas into the stability region of the (√3×√3)R30° phase, this structure is formed ia fast homogeneous nucleation and subsequent lateral growth, resulting in a domain wall network which coarsens on a time scale of several minutes. The subsequent transition into a (1×1) phase upon further decreasing the potential occurs ia instantaneous nucleation at the prevailing domain walls of the (√3×√3)R30° and subsequent one-dimensional growth. Hence, this phase transition depends crucially on the history of the sample, i.e., the density of morphological defects in the (√3×√3)R30° adlayer. On the other hand, the mechanism of the reverse transition from the (1×1) to the (√3×√3)R30° phase is determined by the magnitude of the potential step. Small potential steps lead to heterogeneous nucleation at step edges, whereas for large potential steps homogeneous nucleation and growth predominate.