Refractive index measurements of the Strontium-Barium-Niobate (SBN) crystals show that none of the known second-harmonic-generation scheme (SHG) can be hold responsible for the SHG in SBN. Based on observations of the SHG experiments carried out with several compositions of the crystals in different setup-geometries a new model of second harmonic generaion was developed. The new SHG model, domain-induced second-harmonic generation (DISHG), which considers that the needle-like domain structure of this material plays an active role in the quasi phase matching of the produced second harmonic light has been experimentally proved using two different experiments. The new SHG process in the SBN crystals is a potential light source of cylindrically polarized light. The easy way of obtaining cylindrically polarized light with the SBN crystal broadens the potential applications for this material. The (DISHG) allows to investigate several properties of the ferroelectric domains. Using SHG measurements it was possible to analyze the development of the domain densities for domains of different sizes during the poling of the crystal. SHG measurements allow us to determine the minimum length of the ferroelectric domains. It was shown that this does not depend on the [Sr]/[Ba] ratio and domains are not getting longer after the sample was poled, except for the case of doped SBN. The ferroelectric-paraelectric phase transition has also been investigated. From the inflection point of the nonlinear susceptibility as function of the temperature the phase transition temperature was determined. The non fully-linear dependence of the phase transition temperature as function of the [Sr]/[Ba] ratio can be explained by a system of three different sublattices at the crystallographic positions of Strontium and Barium atoms.