Hole tunneling from an accumulation layer in single-barrier p - type GaAs-undoped AlxGa1-xAs-p+-type GaAs capacitors results in complex current-voltage (I-V) characteristics. At low bias, in the direct tunneling regime, several reproducible voltage-controlled negative resistance regions can occur. I-V curves for a given sample are reproducible while I-V curves for nominally identical samples vary from sample to sample. I-V curves are exponential in voltage with fluctuations in ln(dJ/dV)∼1. Detailed structure in curves of d(lnJ)/dV versus voltage is temperature dependent for T<70 K. At 1.7 K structure in derivative curves is independent of magnetic field. The observed behavior is consistent with the models reviewed by Raikh and Ruzin for incoherent mesoscopic tunneling through states in a randomly nonuniform barrier. The origin of the states in the nominally undoped AlxGa1-xAs barrier is probably Be diffusing from regions of high doping sample growth. © 1992 The American Physical Society.