A simple method is proposed for a parametric construction of characteristic curves using cubic equations of state. This method does not require the resolution of the equation of state for volume or compressibilty factor. For most standard alpha-function formulations, the results are totally explicit. For illustration purposes, this method is applied to the construction of Boyle, Zeno, isotherm inflection, maximum isothermal production and Joule-Thomson inversion curves. (C) 2010 Elsevier B.V. All rights reserved.