Tunneling of electrons between double quantum wells is investigated by time‐resolved photoluminescence in the picosecond regime. The samples contain two In0.53Ga0.47As quantum wells with different widths, separated by various InP barriers. At low excitation density, the luminescence decay time of the narrower quantum well depends strongly on the thickness of the barrier, revealing the lifetimes to be tunneling controlled. A semiclassical model explains the observed nonresonant tunneling escape times. With increasing density, the luminescence decay time of the narrower quantum well strongly increases and finally saturates due to effective mass filtering, which leads to a lineup of the electron levels in both wells and resonant tunneling.