  First we show that any group of automorphisms of null-entropy of a projective
hyperk\"ahler manifold $M$ is almost abelian of rank at most $\rho(M) - 2$. We
then characterize automorphisms of a K3 surface with null-entropy and those
with positive entropy in algebro-geometric terms. We also give an example of a
group of automorphisms which is not almost abelian in each dimension.
