Let K be an NIP field and let v be a henselian valuation on K.
We ask whether (K,v) is NIP as a valued field. By a result of Shelah, we
know that if v is externally definable, then (K,v) is NIP.
Using the definability of the canonical p-henselian valuation, we show
that whenever the residue field of v is not separably closed, then v is
We also discuss the case of separably closed residue fields.