We report on single electron transport through an asymmetric double dot structure with well-defined dot potential profiles. As the two dots are coupled, the conductance exhibits two pronounced types of Coulomb blockade oscillations. An analysis of the small short-period oscillations indicates the presence of interdot interaction. When the coupling strength is reduced, the oscillations become few irregular peaks but they develop into periodic oscillations again as the drain voltage is increased to 0.6 mV. This appearance with increasing drain voltage is well explained by our model which is based on the stochastic Coulomb blockade model and nonresonant tunneling. ©1997 American Institute of Physics.