The paper is treating the local energy decay for several evolution equations associated to long range metric perturbations of the Euclidean Laplacian: the wave, Klein-Gordon and Schrödinger equations. The study is separated by the low and, respectively, high frequency analysis. In low (respectively high) frequency, denoting by \(P\) a long range perturbation of the Euclidean Laplacian, and assuming that for the high energy part that \(P\) is non-trapping, the authors obtain a general result about the local energy decay for the group \(e^{itf(P)}\) where \(f\) has a suitable development at zero (respectively at infinity).