The hyper-Rayleigh scattering (HRS) intensity of two symmetric carbocyanine dyes (1122 DEDC and 1144 DEDC, full names given in the text) in methanol is measured as a function of dye concentration. These dye molecules at equilibrium show a negligible permanent dipole moment. The low concentration data showing that the HRS intensity is proportional to the dye concentration are used to determine the first hyperpolarizability for each of these dyes. However, above a concentration rho(b)=0.1X10(-3) M, the HRS intensity shows an anomalous concentration dependence. Above rho(b), the HRS intensity shows a saturation behavior and it even decreases with increasing concentration at high dye concentration. The depolarization ratio of the HRS intensity is also measured as a function of dye concentration. At lowest concentration, the depolarization ratio is 0.18. As the dye concentration increases, the depolarization ratio also rapidly increases but the increase quickly saturates as the concentration exceeds rho(b). The concentration dependence of the HRS intensity and depolarization ratio are interpreted as due to formation of molecular aggregates. The depolarized Rayleigh scattering (DRS) intensity is also measured as a function of dye concentration. The result of DRS corroborates well with that found in HRS.