Pure eucalyptus oil is extremely volatile. That's part of the reason our bush fires are so bad here in Au.. The leaves (where the oil comes from) burn much faster than the wood of the tree.

I'm not sure how much eucalyptus was in the one that canagirl originally mentioned - "My grocery store ran out of the kind I usually buy so I bought walmart's equate brand with eucalyptus in it"

I'd suggest using care and caution with eucalyptus oil products and make sure it's well diluted. I do the same with tea tree oil too. I'd certainly never use either straight on my skin.