Direct measurements of resonant and nonresonant hole tunneling times in a GaAs/AlxGa1-xAs double-quantum-well structure show that tunneling time at resonance is considerably longer than expected for coherent tunneling or intersubband relaxation. We demonstrate that coherent tunneling and relaxation cannot be treated independently since the coherence is destroyed by collisions and relaxation. This leads to a large increase in the tunneling times observed at resonance. We show furthermore that resonant tunneling due to mixing between heavy- and light-hole states is less important than tunneling between heavy-hole states. © 1990 The American Physical Society.