Performing electronic structure calculations for large systems, such as nanoparticles or metal clusters, via orbital based Hartree-Fock or Kohn-Sham theories is computationally demanding. To study such systems, therefore, we have taken recourse to the hydrodynamic approach to time-dependent density-functional theory. In this paper we develop a variation-perturbation method within this theory in terms of the particle and current densities of a system. We then apply this to study the linear and nonlinear response properties of alkali metal clusters within the spherical jellium background model.