Early stages of oriented overgrowth of Ag, Au, and Pd on thin, single-crystal substrates of mica, molybdenite, Au and Pd were studied by high-resolution electron microscopy and diffraction. Cleaning of substrate surfaces and deposition of evaporated materials were conducted inside an electron microscope. High-magnification, continuous observation during growth permitted investigation of the kinetics of growth. A number of probably elementary epitaxial processes were studied in detail. Nucleation and growth behavior was examined for different supersaturations and free surface energies of substrate and overgrowth materials. The influence of alloying on growth and the spacing of parallel moiré structures was investigated.