We suggest that Type I supernovae result from massive white dwarfs that implode catastrophically at the end of very slow contractions. These slow contractions, which should in some cases require times of the order of the age of the Galaxy, are caused by inverse P-processes that take place in the interiors of the stars. We have found two classes of white dwarfs that could meet the obvious requirements involving the contraction times and the observed frequency of Type I supernovae. The white dwarfs of the first class have masses of about 1.40 M☉ and cores with 10 per cent Mg24. Those of the second class have masses of about 1.20 M☉, Fe56 cores, and intermediate shells with a small concentration of Ca40. Consideration of pre-white-dwarf evolution does not reveal any obvious reason why white dwarfs of either one of the two classes could not be formed. We are thus unable to tell whether Type I supernovae should be identified with Mg24 white dwarfs or with Ca40 white dwarfs. The luminosities of the contracting white dwarfs are estimated and their observability is discussed. The question of the creation of a neutron star in the final collapse is also discussed.