  This note is inspired by the work of Deligne on the local behavior of Hodge
structures at infinity. We study limit mixed Hodge structures of degenerating
families of compact hyperk\"ahler manifolds. We show that when the monodromy
action on $H^2$ has maximal index of unipotency, the limit mixed Hodge
structures on all cohomology groups are of Hodge-Tate type.
