The dynamical structure of nano-plasmas in strongly excited clusters was investigated within a classical treatment via molecular dynamics (MD) simulations. Classical equations of motion of the particles, which are interacting via pseudo potentials, were solved numerically. The dynamical structure factor, which is well understood for bulk plasmas, was generalized via introduction of the bi-local current density correlation function for clusters of different sizes. Free electrons inside the cluster relax within a few femtoseconds into a local thermodynamic equilibrium (LTE). The dynamical bi-local current-density correlation of LTE electrons after short pulse excitation was determined via restricted MD simulations. Several excitation modes were found and characterized, solving an eigenvalue problem. Dispersion relations for resonance frequencies of characteristic modes were investigated. The behavior of the resonance frequency with cluster size as well as plasma properties such as density and temperature were calculated. The collision frequency dependence on cluster extent was discussed. The limits of the used MD model were shown. In conclusion, the generalization of the dynamical structure factor concept going from bulk to finite plasmas was shown and collective excitation properties were discussed.