The effects of various compositions in mixed surfactant solutions of sodium dodecyl sulfate (SDS), an anionic surfactant, and cetyltrimethylammonium bromide (CTAB), a cationic surfactant, at an air-water interface have been investigated using vibrational sum-frequency generation (VSFG) nonlinear optical spectroscopy. The work is focused on understanding the temporal evolution of aggregation behavior of the catanionic system of CTAB and SDS at the charged air-water interface. For the mixed surfactants, the VSFG intensity of the OH stretching bands decreases, whereas that of the CH stretching of alkyl chains increases with time. For the 1:1 ratio of surfactants, the VSFG intensity of the OH stretch vanishes much earlier than the complete growth of the CH stretching modes. Thus, the polar ordering of interfacial water molecules is faster than the time-evolution of alkyl chains of the catanionic system. The temporal growth of the complex between surfactants CTAB and SDS exhibited an induction time (up to similar to 2000 s), followed by a rapid growth (similar to 30 s) and then a slow growth for hours. The effects of different compositions of the surfactants on the induction time and the adsorption kinetics have been investigated. Our results on VSFG are supported by measurements, employing the surface pressure-time (pi-t) kinetics and Brewster angle microscopy (BAM). The nature of pi-t curves and its dependence on composition of surfactants is qualitatively similar to VSFG temporal profiles, except for the absence of the rapid adsorption growth in the former. This difference in the adsorption kinetics is explained based on formation of surfactant domains, as detected by BAM, at the air-water interface.