A general procedure is given for calculation of time correlations in liquids, including complex multitime functions, with instantaneous normal modes (INM). The method requires equilibrium averages only and eliminates any need to invoke a fictitious harmonic well. The third and fifth order optical response functions, and the self- and collective-density correlations, are obtained and compared with the results of other methods. INM provides several advantages for evaluating the nonlinear response function required for fifth-order scattering. The time expansions of the response functions, and the role of anharmonicity, are discussed.