A simple Landau-Ginzburg Hamiltonian is proposed to study an example of critical behavior in ionic systems. We focus on the role of asymmetry between ions which is common in real systems. The free energy calculated via a functional integration contains a divergence due to the Coulombic self energy. The finite part is just the Debye-Huckel limiting law with the correction due to the asymmetry. The criticality in our model is associated with an attractive non-Coulombic interaction between ions whatever their sign. At the level of our model there is no criticality for the restricted primitive model. The correlation functions are calculated. Out of the criticality the charge-charge correlation function conforms to the Stillinger-Lovett conditions and the charge-density coupling vanishes in the long wavelength limit. At the criticality due to the asymmetry the effective density of free charge carriers has to be reduced to verify the second Stillinger-lovett condition and the charge-density correlation function exhibits a long wavelength coupling.