The electrocrystallization and growth of Te and CdTe under potentiostatic conditions have been studied using the theories developed for the electrocrystallization of metals on foreign substrates. The electrodeposition of Te on glassy carbon and of CdTe on tin oxide coated glass take place by progressive nucleation/three dimensional growth under diffusion control, whereas the electrodeposition of CdTe on monocrystalline silicon takes place by instantaneous nucleation/two dimensional growth under kinetic control. From considerations of progressive nucleation/three dimensional growth under diffusion control, a new analytical equation to express increase in current with deposition time is proposed. The dependence of saturation nuclear number density on temperature is also discussed. Computer simulations of instantaneous nucleation/hemispherical growth under diffusion control have been carried out using the three dimensional diffusion limited aggregation technique. The simulated current transients are compared to analytical expressions. Photoeffects during electrodeposition have also been studied. The results show that the CdTe deposit behaves as an amorphous insulator with a high density of bandgap states.