  Our knowledge of the shape of radial metallicity gradients in disc galaxies
has recently improved. Conversely, the understanding of their time evolution is
more complex, since it requires analysis of stellar populations with different
ages, or systematic studies of galaxies at different redshifts. In the Local
Universe, Hii regions and planetary nebulae (PNe) are important tools to
investigate it. We present an in-depth study of all nearby spiral galaxies
(M33, M31, NGC300, and M81) with direct-method nebular abundances of both
populations. For the first time, we also evaluate the radial migration of PN
populations. We analyse Hii region and PN properties to: determine whether
oxygen in PNe is a reliable tracer for past interstellar medium (ISM)
composition; homogenise the published datasets; estimate the migration of the
oldest stellar populations; determine the overall chemical enrichment and slope
evolution. We confirm that oxygen in PNe is a reliable tracer for the past ISM
metallicity. We find that PN gradients are flatter than or equal to those of
Hii regions. When radial motions are negligible, this result provides a direct
measurement of the time evolution of the gradient. For galaxies with dominant
radial motions, we provide upper limits on the gradient evolution. Finally, the
total metal content increases with time in all target galaxies, with early
morphological type having a larger increment Delta(O/H) than late-type
galaxies. Our findings provide important constraints to discriminate among
different galactic evolutionary scenarios, favouring cosmological models with
enhanced feedback from supernovae. The advent of extremely large telescopes
will allow us to include galaxies in a wider range of morphologies and
environments, thus putting firmer constraints to galaxy formation and evolution
scenarios.
