It's either a caterpillar (2 to 5 pair prolegs) or a sawfly (6 to 8 pair prolegs). Both eat leaves, so watch it.

You might also contact the folks at your county's Extension Service office as those folks are likely to be familiar with what it is. (Then return to tell us, please.) You can locate that office with this interactive map:

http://npic.orst.edu/pest/countyext.htm

Citrus Fruit Piercer (Gonodonta nutrix), a moth caterpillar.

http://bugguide.net/node/view/70388/bgimage

http://butterflies.heuristron.net/moths/gonodontaNutrix.html

your photos show two different instars, or larval stages.

Ty so much. That's it looks like I have to live with it and hard to get rid off. They do look gorgeous.