I think you may have slugs. You can find out for sure if you take a flashlight out after dark and look at your plants.

You can use Safers Slug and Snail bait. It is made with Iron Phosphate and is approved for Organic farmers. It won't harm birds or pets. Some have had success with beer, but it never worked for me. Going Organic doesn't mean you have to let the bugs eat your plants even if they are your vegetables. There are things and recipes you can use. All you have to do is find out what's causing the damage and look up what to do about it.

Go out in the evening to do some sleuthing for culprits, even if you have to take a flashlight. That's a good time of the day to find chewing pests. You haven't given us enough information to make a guess.

Thanks oilpainter and rhizo. I will be on the lookout and use a flashlight at night to see what's up and then will do research to find out the best methods.
Susan.

Japanese Beetles love zinnias a lot. I monitored my zinnias last year and saw tons of jap beetles. I am seeing many JBs now in my garden. I'll be spraying Sevin tomorrow.

Sevin as a brand name for carbaryl, which is toxic to bees and many other beneficial insects, as well as to its target pests. That's the problem with chemical controls.