  Bielliptic and quasi-bielliptic surfaces form one of the four classes of
minimal smooth projective surfaces of Kodaira dimension $0$. In this article,
we determine the automorphism schemes of these surfaces over algebraically
closed fields of arbitrary characteristic, generalizing work of Bennett and
Miranda over the complex numbers; we also find some cases that are missing from
the classification of automorphism groups of bielliptic surfaces in
characteristic $0$.
