  In the past few decades, observations have revealed signatures of metals
polluting the atmospheres of white dwarfs. The diffusion timescale for metals
to sink from the atmosphere of a white dwarf is of the order of days for a
hydrogen-dominated atmosphere. Thus, there must be a continuous supply of
metal-rich material accreting onto these white dwarfs. We investigate the role
of secular resonances that excite the eccentricity of asteroids allowing them
to reach star-grazing orbits leading them to tidal disruption and the formation
of a debris disc. Changes in the planetary system during the evolution of the
star lead to a change in the location of secular resonances. In our Solar
System, the engulfment of the Earth will cause the $\nu_6$ resonance to shift
outwards which will force previously stable asteroids to undergo secular
resonant perturbations. With analytic models and $N$--body simulations we show
that secular resonances driven by two outer companions can provide a source of
continuous pollution. Secular resonances are a viable mechanism for the
pollution of white dwarfs in a variety of exoplanetary system architectures.
