Eucalyptus branches, I think, are preserved by standing them in glycerin. The branches soak up the glycerin and then they don't dry out and become brittle. This may be what is oozing out. Maybe you could try using a spray-on polyurethane on the backs of the arrangements to seal them.

My eucalyptus wreath did the same thing! It looked as though it had bled down the wall. I washed the wall with a Clorox solution and then repainted, but the stain still showed through. I had to use a primer and then paint over it again. I don't know why the wreath decomposed this way, but it was strange!

Glad I checked in here! I have some eucalyptus that I bought a few months ago and wanted to make a swag, however, at the time I just threw the branches in a tall vase and sat them in my room. Glad I did now! I was thinking of making a swag for my friend out of it but best not now. She's renting and doesn't need a mess like that.

~Leslie~

It's a substance that is part of the eucalyputs leaves. When I lived in California I had a pool surrounded by eucalyputs leaves. Had to be very vigilant about not letting any of the leaves settle on the bottom of the pool (even one), because they immediately left a stain on the bottom of the pool.