This may be of help

Here is a link that might be useful: Caterpillars identification guide

They are probably swallow tailed Butterflies, The Black ones, Spice bush maybe, don't kill all of them, let them do their thing. They will eventually pupate ,when they do take 'em inside and let the kids watch until they metamorphose into , what else, butterflies. Try it I did it several years ago ...Had swallowtails flying all over the den.

If you include images, someone will be able to ID your caterpillars for you. Very early instars of the Black Swallowtail caterpillar (aka: parsley cat.) are dark with a white belly band. As they get larger, they evolve into what is arguably one of the prettiest caterpillars around! See attached link for a google page, just for comparison. Doesn't really match your description, does it?

Here is a link that might be useful: parsley caterpillar

Check this site also,
http://en.wikipedia.org/wiki/Black_Swallowtail

Here is a link that might be useful: http://en.wikipedia.org/wiki/Black_Swallowtail

Wouldn't you just know it? I planted my parsley specifically to attract the butterflies and haven't seen a single caterpillar. You don't want them and get them.
kay

Me, too, nothing has touched my parsley OR my fennel this year. Both should be nubs by now. I've hardly seen any butterflies.

I guess we're not going to get any pictures or further information from mimi.

They look like the ones at the "parsley caterpillar" link given, except mine are a grayish white instead of the green. I took or posted no picture because I've been told we aren't allowed to upload photos here. If I was told wrong, someone please direct me to the info for doing so in future. Thanks to everyone for all the info. Whatever they are, they're gone now, albeit so are 2/3 of the leaves. (may have chased 'em out when I flushed the plant with fresh water) We have butterflies here, but numerous kinds so not sure what these became