It sounds like you have spiraling whitefly. My neighbors and I also had a terrible infestation. After trying organic sprays without success, I finally used Bayer Advanced and a strong water spray with a hose. That did it. Make sure you spray well under all the leaves and use the Bayer Advanced according to instructions. My infestations were on my coconut palms and hurricane palms. Crab spider webs seem to catch quite a few adults, so leave those be. It's the larvae that do the damage though on the underside of the fronds. Spray them all off.

Spray hard every day.

The trick to getting whiteflies is how to spray and when to spray. If you're diligent, you can knock down an infestation with water only. These rotten bugs develop immunity to pesticides at the drop of a hat apparently, so "manual" removal methods are the best.

In the evening or early morning (when the little ***kers are sleeping) you need to "upside-down" water all affected plants. This means spraying the underside of the leaves. This basically drowns them as they cannot tolerate water (that's why they're under the leaves, protection from the dew)

You're going to have to do this daily until you start seeing a difference, then you can start cutting back. I do the evening, cuz I'm too lazy to get up while the dew is still on the ground, but if your plants may be susceptible to moisture problems if wetted in the evening, the AM duty may be the way to go. The good thing is, you'll see them burst in clouds upward when you hit the plants... and every day you'll see fewer and fewer.

I always "upside-down water" at least once a week as a preventative.

alys,

That is good to know. I've had some whitefly problems as well. Bayers worked for me, but I don't want them to develop immunities. I'll try spraying the undersides of the leaves.