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I am not 100% sure if this worm is actually a Cabbage Worm or not, but it looks similar. I keep as on top of insect pests in the vegetable garden and flower beds the best I can, and I have allot of help with worms from wasps. A neighbor gave me a couple of her 30" tall Coleus and I put them in pots and took them to one of my sun rooms and moved them the the front porch as temps permitted. I never noticed any parasite problems. When the weather forecast predicted below 20 degree temps coming, I moved the Coleus to the library... There has been some leaf loss in the sun room due to a change in location, but more started falling off in the library...allot more! When the temps moved back up in the 30's, I took the Coleus into the kitchen to remove all the dying leaves and noticed these Cabbage Worm-like critters eating away at the veins on the bottom of a few of the leaves... I suppose the warmer room caused eggs to hatch?!?!
Another thing is that I notice that some of the smaller leaves that have died are hanging on the plant by a string...like a spider web. What is causing that?
It says I am in St. Paul, Minnesota... I am now in Leland, Mississippi so I have to edit my profile!
If you can, provide an image of the caterpillar(s), as there are several species having an appearance similar to what you describe. Even then, a positive specific identification may not be possible. Regardless of its identity, any pesticide containing the bacterium Bacillus thuringiensis var. israelensis (Bti) should effect control. As for the other problem, use a magnifying glass to examine the leaves to see whether there is a very fine webbing along with minute living critters walking about (see http://tinyurl.com/yjeyj2m for an image). If this is what you find, you may have spider mites, although from what I have read on the subject, coleus plants do not seem particularly susceptible to these pests. Application of an insecticidal soap usually will control these.