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Numerical studies of transient and steady state one-dimensional transport through resonant tunneling structures (RTSs) have been widely reported. For the most part, the structures studied have been symmetric and single welled. Following the method of Buot-Jensen, we apply a lattice Weyl-Wigner 1D single band transport code to both double barrier (DBRTS) and triple barrier (TBRTS) GaAs/AlGaAS structures which are spatial asymmetric (barrier/well thicknesses). Both the transient and steady state behaviors are studied. Preliminary results show that the current-voltage characteristics (a) vary drastically from those obtained from the associated symmetric structure.