The quality or state of being stubbornly unyielding: bullheadedness, doggedness, mulishness, obstinacy, obstinateness, pertinaciousness, pertinacity, perverseness, perversity, pigheadedness, tenaciousness, tenacity, willfulness.

Is hard headed one word or two?

or hard-head·ed

not easily moved or deceived; practical; shrewd. obstinate; stubborn; willful.

Is strong headed one word?

determined to have one's own way; willful; stubborn; obstinate: a headstrong young man.