  Sphalerons -- unstable static solutions of classical field equations in
(d+1)-dimensional space-time -- may be viewed as euclidean solutions in d
dimensions. We discuss their role in the large order asymptotics of the
perturbation theory. Specifically, we calculate their contribution to the large
order behaviour of the ground state energy in a quantum mechanical model. When
the number of negative modes is odd, single sphaleron contribution dominates,
while this contribution vanishes when the number of negative modes is even.
These results are confirmed by numerical calculations.
