It sounds like fasciation, although a picture would confirm it.

If so, you can cut off the strange growth.

I have seen something that sounds like the same thing and I attributed it to a severe outbreak of Woolly Apple Aphid. Did these trees receive a dormant oil application?

I haven't applied anything to it except water and fertilizer.

I'm not sure how to post photos in a message. Do I use the URL link? Do I put them in the gallery first?

I uploaded a photo to the Garden Gallery, and hopefully I can link to there:

Here is a link that might be useful: I find this totally fasciating!

yes, I have seen that and I was told that it was caused by aphids somehow. I think they mentioned virus. I don't remember who told me and I can't vouch for it, but I do know the trees were afflicted by aphids. It doesn't look to me like you need that branch and I would cut it out and apply a dormant spray of oil and lime sulfur. Woolly Apple Aphids leave a white cottony substance on the trees. Ever see that? And they can also be a big problem on bushy trees. It seems sunlight and, I guess, air circulation will help to curtail it. for my money it is not serious, but you need to prune and spray.

Thanks, Geraldo. There's no doubt they're getting plenty of sun and air! This is a windy desert here! No, I haven't seen any cottony growths on them. My two surviving apple trees have already been pruned heavily -- more than half of the branches died because of flat-headed borers, and the surviving ones have dozens of holes. I will be pruning those growths. Today I painted the trunks with white latex. I think we're making progress!

No aphids. No virus.

As I said earlier, fasciation. Cut it off.

Jean is right. Cut it off. A malady brought about by any number of things. I never knew what caused that.