Oleander Hawk Moth (Daphnis nerii) by ©od0man/Steve Covey    The caterpillars feed mainly on oleander (Nerium oleander) leaves, a highly toxic plant to which toxicity they are immune.    The adults feed on nectar of a great variety of flowers. They have a preference for fragrant species like petunia, jasmine and honeysuckle. They are especially active in the twilight time, hovering over the flowers after sunset.