Hi,Deb.
These caterpillars feed exclusively on Oleanders. They are poisonous and can defoliate the bush rather quick.
Please click on the link,below for pictures and further information.
On my Oleander,I let them eat all they want. I enjoy what ever flowers they leave behind and enjoy these beautiful, winged creature.
Happy gardening!
Felix

Here is a link that might be useful: Oleander Caterpillar

They will also eat the ends or buds and you will have no flowers, I spray constantly to keep these nasty pests off of mine, I also use systemic, however the spary is faster and immediate..

I didn't plant Oleander where I live now, 'cause I saw what happens to them from bugs/worms at my last house. I hate spraying insecticide! It is a pretty plant though.

Oleander Moth/Caterpillar is NOT poisonous or stinging. They just look that way. The also eat the native yellow mandevilla vine. I will only spray if the population gets out of control, usually there is enough flowers for me and leaves for them. The moth is really striking with its dark blue/black body and wings with white spots. It is worth having some ratty looking oleander or yellow mandevilla to see the adult moths.