The authors prove that up to isotopy a 2-bridge hyperbolic link has just two unknotting tunnels, namely the upper and the lower one. A tunnel is called strongly parabolic, if the fundamental group of the complementary handle body defined by the tunnel is generated by two elements which can be freely homotoped to the boundary and represent parabolic isometries. The upper and lower tunnels of a hyperbolic 2-bridge knot or link is shown to be strongly parabolic and isotopic to a geodesic arc bounded by \(\log 4\) relative to the canonical cusps.