The origin of magnetic fields observed in circumstellar envelopes and proto-planetary nebulae is investigated theoretically. The build-up region of these fields is likely to be found deep in the progenitor (assumed to be an asymptotic giant branch red giant). With toroidal fields ~106 G produced by a dynamo mechanism in the degenerate core (roughly assimilated to a white dwarf of mean radius ~109 cm), we find values ~50 G in the convective envelope (mean radius ~1013 cm) and 1 mG in the circumstellar envelope (mean radius ~1016-1017 cm). A model for the ejection of massive winds is presented. We point out that the two phenomena (magnetic activity into the degenerate core and ejection of gas by the star) could be strongly interrelated.