Little black bugs sounds like it might be aphids...

Mites are mainly found on the underside of leaves and they are tiny, barely visible. If you blow on them, they get pissed and start to move around. The leaves take on a yellow mottled appearance.

Aphids sap away the plant's energy, and what happens is that new growth comes out weak and distorted.

In my experience, soapy water sprayed consistently for a few days is enough to get rid of a minor mite infestation. Make sure you concentrate in spraying the undersides of leaves. Soapy sprays don't always work as well against aphids. If you spray hard enough, you can knock them off. Some species don't mind cold weather either, so putting the plants into the garage may not help.

Horticultural oils added to the soap are much more effective against aphids. You can try adding canola oil, it works quite well too.

Can you post some close-up photos so we can help ID the culprit?

For over 25 years I have fought mites, aphids, scale and mealy bug on a large collection of indoor plants. This year is the first year I have no pests! The reason...... I quit using insecticides and started using insecticidal soap. This did the trick. I have large banana plants, hibiscus, palms, elephant ears and other tropicals. I haven't seen any bugs yet since Fall. Good luck!

Thank you both for your input. I googled pics of aphids, but it looks like they're a lighter color, yellowish green or white. The bugs that are on my palms are black. I'll try to post pics tomorrow.

The only thing i have ever used and ( it works great by the way )is expert from wal mart It's cheap and it does a great job !

Check out black aphids here

They most certainly can be black

For mites, aphids, etc. use GreenLight Bioganic Home & Garden Insect Spray. It is 100% organic and safe around children and pets. I have used it with good success to kill aphids and ants on my yellow Malayan Dwarf and Mexican Tall coconut palm sprouts. Everybody needs to start using more organic fertlizers and sprays to control pests. They are better for us, for our plants, and for the environment.

Xerophyte, I believe you're right, they're aphids and are not on the underside of the leaves like mites would be.

Thanks coconut palm. I'll have to take a look for it.

If you have your plants in a place like a garage or shed, and you do not want to use any chemicals to get rid of the aphids, LADY BUGS will do the job for you. The few times I have had bad aphid infestations ( on outdoor plants) I have purchased lady bugs, and they took care of it. Lady Bugs eat aphids... ALOT of aphids. They dont just fly off either, if there is a good food source, they definitely stick around. My aphid woes were gone in just a week.

I know around here they sell lady bugs at garden centers in containers. usually 100 or so in a container. Only problem is, they only really sell them in spring and early summer.

Just a thought. =o)

Thats good to know we have hundreds of them here.

I use Safers Houseplant Insecticide as I found that is the only product that actually works. If I had a large infestation I would probably order from this company. See link.

Here is a link that might be useful: safe insect control