Tunneling between two narrow quantum wells with different effective masses is proposed as a probe of the quasiparticle inelastic lifetime at finite excitation energy. Conservation of energy and of kជ, the momentum parallel to the interface, allows the tunneling conductance to be large only if the crossing of the two energy bands ͓E1(kជ)ϭE2(kជ)ϩeV͔ at an applied voltage V occurs between the two Fermi levels. The abruptness of the change in tunneling current as this crossing passes through one of the Fermi levels can be used to investigate the lifetimes of the quasiparticle states involved. Results based on the random phase approximation are used as an illustration.