Scientists planning to study the bugs say there will be another problem - a bad stink after they all die!
Gardeners have also been advised to use nets to protect trees and shrubs.
The bugs will lay their eggs by cutting slits in tree bark, and these should hatch after a few days.
The young will burrow into the ground - to emerge in 2021.
The bugs are meant to be very stupid, and easy to catch - good news for people who like to eat them.
Apparently they taste like tinned asparagus, although we don't recommend you try one!