Ion conduction in one-dimensional cationic conductors potassium priderite single crystals K1.6Mg0.8Ti7.2O16(KMTO) and K1.6Al1.6TI6.4O16(KATO) was studied by impedance spectroscopy between 10 Hz to 99 GHz. The real part of the complex conductivity is approximately constant in the microwave frequency region. It is found that two partial thermally activated conduction processes contribute to the ion conduction at microwave frequencies. One corresponds to the ion conduction process across the perturbed intrinsic barriers with a period equal to the lattice constant along a c-axis.