If the North and South pole pieces are already at the pole positions but not correctly oriented, then bring them to the equator by D3 R1 U3. Rotate the equator to bring the North pole piece to the front. In this phase the actual position of the pieces on the equator is ignored. Note that on the Equator puzzle, you can choose a monochrome piece as one of the two pieces if necessary. Turn the equator to bring one of the two twisted pieces to the front.
Repeat steps a-c as often as possible.
On the Equator puzzle, all pieces will now be correctly oriented because of the monochrome pieces. On the Hungarian Globe you may still be left with one antipodal pair that needs a half turn. To rectify this, use the first or third sequence above to twist the pair a quarter turn, together with any other pair. You now have two pairs which need a quarter turn, so you can again use the first or third sequence to twist those two pairs correctly. The phase is actually quite easy, but hard to explain.