  Cosmologies with running cosmological term (Lambda) and gravitational
Newton's coupling (G) may naturally be expected if the evolution of the
universe can ultimately be derived from the first principles of Quantum Field
Theory or String Theory. In this paper, we derive the general cosmological
perturbation equations for models with variable G and Lambda in which the
fluctuations in both variables are explicitly included. We demonstrate that, if
matter is covariantly conserved, the late growth of matter density
perturbations is independent of the wavenumber. Furthermore, if Lambda is
negligible at high redshifts and G varies slowly, we find that these
cosmologies produce a matter power spectrum with the same shape as that of the
concordance LCDM model, thus predicting the same basic features on structure
formation. Despite this shape indistinguishability, the free parameters of the
variable G and Lambda models can still be effectively constrained from the
observational bounds on the spectrum amplitude.
