  We give a simple argument to prove Nagai's conjecture for type II
degenerations of compact hyperk\"ahler manifolds and cohomology classes of
middle degree. Under an additional assumption, the techniques yield the
conjecture in arbitrary degree. This would complete the proof of Nagai's
conjecture in general, as it was proved already for type I degenerations by
Koll\'ar, Laza, Sacc\`a, and Voisin and independently by Soldatenkov, while it
is immediate for type III degenerations. Our arguments are close in spirit to a
recent paper by Harder proving similar results for the restrictive class of
good degenerations.
