might be mealy bugs?

http://paddy1.over-blog.com/article-mealy-bugs-look-like-small-patches-of-cotton-wool-113519131.html

Hmm...I agree with Raimeiken, it DOES sound like mealybugs. You can google for images or look in books/magazines etc too. Can you post a pic or three? Let us know what you think, good luck!

Thank you so much for your replies. The top set of photos in the link Raimeiken helpfully provided don't look at all like this infestation. I've had what I assumed were mealybugs on house plants and had my outdoor thing looked like those photos, I might have recognized it as such. BUT, the middle photo on the bottom set of six pictures does look like what's outside. Perfectly round — no tendrils indicating the white mess was spreading. Just individual round balls of pure whiteness. So maybe that's the newly laid eggs? I never noticed any other substance that followed the white balls, just more and more white balls that didn't go away until there was a chill in the air.
When things started coming back this spring, the plants seem to show no ill-effects from last year's infestation.
In any case, I will try one of the homemade sprays suggested in the second article the photos link to. Heaven knows we have easy enough access to hot peppers in Arizona! I'll try to pulverize them with the garlic and other ingredients specified in that article in my Nutribullet. And I'll give the two infested plants a good spray. Right now I only see this thing on two plants in the yard, whereas last year it appeared on many in the front and back yards. So some remediation will be easy at this time.
Thanks again for your help.

glad to help. keep us updated if the home remedies work.

Wow! Yes, kevininphoenix, that's EXACTLY what the stuff on my plants looks like. Not 1 in 12 like the photos of the mealybugs. I wasn't able to see the link you provided, so I just Googled spittlebugs and many pictures were provided. Not only do they match exactly what's on my plants, they are attached to the stems in exactly the position show in the photos. The descriptions I read noted they did no permanent damage to the plants, which is also what I noticed from having them last year.
The only thing that doesn't match is the statement that says they lay their eggs in late summer (what happened last year), yet these have appeared in February, but nothing seems normal about growth in my neighborhood this "spring," so I will try the hose as a first line of attack.
Thanks very much.

Good suggestion, Kevin! Thanks too for the confirmation, jukes. My rosemary plants get quite a few spittle bugs in mid-spring/early summer. I just let them do their thing and make sure to REALLY wash the rosemary before using in the kitchen, hah. Great discussion! Happy gardening all!

One of the easiest ways to get rid of them is to spray them with a mix of water and liquid dish detergent ... about a teaspoon in a quart spray, a tablespoon in a gallon. Wet the plants thoroughly

It breaks the surface tension and dehydrates the bugs.

Grant_in_AZ: My brother was over yesterday and I showed him the spittlebugs. The first thing he said was, "Oh, yeah, I have those on my rosemary every year." He has huge rosemary plants in his backyard. They even named their dog Rosemary because when she was a puppy she would roll in the plants looking for bugs to attack and she smells like rosemary all the time. His rosemary couldn't be any bigger or healthier looking, so I guess spittlebugs aren't that bad to have.

They must have a thing for herbs!

Glad I could help :-D

I have 4 rosemary plants in my back yard and I've seen those on it every year. Never knew what they were until now. Thanks!

I'm weighing in months too late to be relevant, but I have spittlebugs on my rosemary too, so it is a relief to know I'm not alone. I do notice that if they are on or near new growth, the tips droop, which I presume is competition for moisture in the plants vascular system.

BTW, don't forget you can take a promblematic bug or sprig in a sealed ziplock bag to the University extension service. They have highly informed master gardeners equipped with a reference library to help you (and some interesting idea/display gardens). They are on Campbell Avenue opposite Trade Joes, a few feet before the bridge over the Rillito. I think they are open M-f, 9:00 - 5:00.

Happy xeriscaping!