Every year, in the spring, your Eucalyptus will under go a change of foliage. The old leaves will be shed and new foliage produced. To do this, the tree sucks out all the stored nutrients in the old leaves, held on the lower part of the young tree. These go spotty, get black spots, turn beige/biscuit/red/yellow/brown or all of this and then drop off. This is completely normal. Lower branchlets may go brown and sticky, at which point you can cut them off.