From the viewpoint of unstable growth of nonequilibrium fluctuations, nucleation processes were examined. Electrostatic equilibrium produced by the electric double layer is always locally broken by the thermal motion of solution particles. This breakdown, i.e., fluctuation occurs not at the Nernstian equilibrium, so that we call it "nonequilibrium fluctuation." In examining the mechanism of the fluctuation, it was shown that a new type of instability occurs, which takes place in the absence of the intense specific adsorption of ions on the electrode surface. Then, two different modes for the instability are possible, that is, one is the case where from the beginning, there is no specific adsorption, and another the case where the surface is specifically adsorbed by the ions at the initial stage. The former case allows the fluctuation to continuously transfer from the stable state to the unstable nucleus growth whereas in the latter case, immediately after specific adsorption ceases, nucleation starts rapidly. On the contrary, when the specific adsorption occurs at the nonspecifically adsorbed surface, nucleation will be suddenly stopped. Furthermore, the fluctuation of the second type is formed for the mass flux of depositing metal ions in the diffusion layer, which becomes always unstable, accompanied with the unstable growth of the fluctuation of the first type.