Abstract : The very high energy γ-ray spectra of Pulsar Wind Nebulae are interpreted as due to inverse Compton scattering of ultrarelativistic electrons on the ambient photons, whereas their X-ray spectra are due to synchrotron emission. We investigate the relation between the γ- and X-ray emission and the pulsars' spin-down luminosity and characteristic age. We find that the γ-to X-ray flux ratio of the nebulae is inversely proportional to the spin-down luminosity (~Ė-1.9) and to the characteristic age (~τc2.2) of the parent pulsar. We interpret these results as due to the evolution of the electron energy distribution and the nebular dynamics, supporting the idea of so-called relic pulsar wind nebulae. These empirical relations provide a new tool to classify unidentified diffuse γ-ray sources and to estimate the spin-down luminosity and characteristic age for four rotation powered pulsars with no detected pulsation from the X- and γ-ray properties of the associated pulsar wind nebulae.