Carrier transfer in InAs/ GaAs asymmetric quantum dot pairs has been studied by means of continuous-wave and time-resolved photoluminescence in a bilayer InAs/ GaAs quantum dots system. The dependence of the tunneling time on the thickness of the separation layer is determined and the tunneling time is found to span the range from 250 to 2500 ps. A microscopic model of carrier transfer, including nonresonant electron tunneling from a direct into a cross exciton state, with subsequent generation of two direct excitons in adjacent quantum dot layers, is proposed.