In this work, Cu2O nanopyramids and CuO nanoflakes are synthesized using simple co-precipitation and hydrothermal methods, respectively. The XRD and Rietveld refinement results show that the synthesized samples are pure single phases of cubic Cu2O and monoclinic CuO. The field emission scanning electron microscope (FE-SEM) is used to figure out the size, shape and surface morphology of the materials. The alternating current (AC) conductivity (σac) of the Cu2O and CuO nanostructures was investigated and explained in the framework of the correlated barrier hopping model. Maxwell–Wagner model was applied to explain the behavior of the dielectric constant as a function of frequency. The impedance spectra show that the grain boundaries play an important role in the dielectric relaxation processes. The obtained Cole-Cole diagrams were explained using the Maxwell- Wagner capacitor model.