Is there any period during which the nerve is not responsive to stimulus?
I thought it's absolute refractory period..
Is it?

Yes, I would agree it's the absolute refractory period, followed by a relative refractory period until the resting potential is restored to normal. This is true of "excitable membranes" such the axonal membrane or the cell membrane of the heart's Purkinge fibers. It relates to the flows of ions (chiefly Na⁺ and K⁺) as the action potential completes its cycle.