The transport properties of 0.75 &mgr;m long insulating indium oxide wires and rings have been measured. These devices have no apparent tunnel barriers, yet they exhibit two properties which are characteristic of series arrays of small capacitance tunnel junctions: highly non‐linear IV characteristics and a zero‐bias conductance which is periodic in a voltage applied by means of a lateral gate. Two types of samples can be distinguished based on the behavior of the conductance oscillations at low temperatures. For the first type, the structure of the oscillations remains periodic down to our lowest temperatures, similar to the data from the tunnel junction arrays. For the second type, lowering the temperature results in a transition from periodic to quasi‐periodic conductance peaks. The temperature and magnetic field dependence of these effects suggest that they are due to the influence of single electron charging on transport through localized electron states in the indium oxide.