Regular and wooly aphids... spray with liq. dish soap. 1 table spoon in a gal. of water mixed up and not in the hot sun. Repeat in 7 days(they reproduce about every 7 days) The soap suffocates them and they will die.

Unfortunately, woolly aphids also live on the roots -- no treatment deals with that. Some apple trees will decline because of the root damage, other apple trees will still produce enough to keep the home gardener happy.

Depending upon your goals, you might prefer to replace with a resistant apple.

I'll probably go ahead and try the dish soap on the crown of the tree. I like that plan better than a harsh pesticide. We'll see what happens and whether or not it manages to cope. This is a tree that my son started from seed so I want to do what I can to preserve his experiment. I warned him that we have no idea whether the apples will be any good and that it probably won't produce for many years but he still wanted to do it. We also have a domesticated Gala Apple. So that's what I'm counting on for actual apple production. Hopefully they used aphid resistant root-stock for that one. No sign of aphids on it as of yet.