Elisabeth, I appreciate your trying to help. It isn't either of those. It is very small and smooth with no hairs or fuzziness at all. I am a total newbie at trying to identify caterpillars but I have seen some beautiful butterflies this year and didn't want to kill anything. I did some extensive searching around the net and couldn't find anything similar. It doesn't look anything like the caterpillars I saw for some of the wonderful butterflies.
Thank you again.

Could be Beet Armyworms which are known to attack Sunflowers, among many other things. The "smooth" appearance is a dead giveaway to me that it is some kind of moth larva.

Are you finding them in groups, or just solitary cats on the plant?

Sometimes an image may not look exactly like the caterpillar you have because they can present differently depending on what they are eating, time of year, region, many other things influence the caterpillar coloration.

Susan

Here is a link that might be useful: {{gwi:489549}}

That really helped me, thank you so much. I looked up beet armyworm and that led me to southern armyworm which is what it turned out to be. I can't believe how much it can eat!! Now I need to figure out what to do about it, hopefully with no chemicals. I wonder if insecticidal soap would work?

You can just toss them in a bucket of soapy water if you can detach the leaf or leaves they are congregating on. That way you won't make the foliage unpalatable or deadly for other caterpillars that you may want, like the Silvery Checkerspots that Elisabeth mentions, or possibly Gorgone Checkerspots, or even Bordered Patches, altho I don't know if you get these in your area.

I agree with Elisabeth, tho, about usually finding solitary caterpillars rather than groups of them. But maybe they start out in a group and then disperse. I'm really not all that familiar with them, other than to schmoo the ones I find on my tomato plants.

Glad we could help you out!

Susan

I really appreciate the help. I hope my sunflowers will come back from this and get new leaves. I am going to keep checking and pick off all I find. Its so disappointing when you grow something from seed just to see it eaten up.
Blessings,
Susan.

I sympathize. I don't even try to grow sunflowers anymore. The groundhogs and rabbits eat them before they can even get going. Last year I thought I had succeded with two feet of growth, only to come out one day and they were mowed down. One of these days the electric fence will be installed! Good thing they don't keep out butterflies!
-Elisabeth