The response function of an interacting fermion gas is considered in the entire (k-->,omega) space. Applying a generalized linear response theory, it is expressed in terms of determinants of equilibrium correlation functions, which allow for a systematic perturbative treatment. The relation to dynamical local-field factors is given. As a special case, the dielectric function is evaluated for two-component (hydrogen) plasmas at arbitrary degeneracies. Collisions are treated in Born approximation leading to a (k-->,omega)-dependent collision integral. The link to the dynamical conductivity is given in the long-wavelength limit. Sum rules are discussed.