The growth and structure of Pd alloys formed on Cu(100) have been studied from the initial nucleation to the formation of a second-layer structure, using scanning tunneling microscopy (STM) and Rutherford backscattering spectroscopy (RES). The STM images show that individual Pd atoms initially alloy into lattice sites of the substrate, with a preference for occupation of second-nearest neighbor (NN) sites. This results in the formation of short, [001] and [010]-directed chains of Pd atoms which converge to form a c(2 x 2) structure as the coverage is increased. Copper atoms ejected by the incorporation of Pd into the surface form Cu islands on the terraces. The growth of such islands on the alloyed terraces results in subsurface Pd, and consequently, a greater amount of Pd is required to form the c(2 x 2) structure than the ideal 0.5 monolayer (ML). Nucleation of the second Pd layer is seen at upper step edges before the first layer c(2 x 2) structure is completed. Continued deposition of Pd results in completion of the c(2 x 2) structure and further growth of the second (topmost) layer phase which from LEED appears to have a p4g symmetry, while a p(2 x 2) periodicity is revealed by STM. A model is proposed in which the second layer is a mixed alloy layer of Pd and Cu forming on top of a p4g reconstructed c(2 x 2) first layer.