What you have is a green lacewing. Do not kill these insects they are very beneficial! Here is what I have in my field guide: "Females lay white eggs suspended at the end of slender stalks. The larve are sometimes called aphid lions because they prey on aphids and other soft-bodied insects. Pupation occurs in egg-shaped, silken cocoons that are attached to plants." Hope this helps. ---- Party on Dude!