Though not working toward an imminent transition to a monetary or currency union, the Central American Monetary Council (or CMCA, from Spanish Consejo Monetario Centroamericano) serves as an institution promoting economic and financial stability among five Central American countries (Costa Rica, El Salvador, Guatemala, Honduras and Nicaragua) and the Dominican Republic. Econometric studies conducted by researchers from CMCA have mostly focused on studying inflation levels of these countries, making use of econometric tools such as VECM and cointegration. We expand the study of inflation stability in the member countries of the CMCA by adopting a long memory and fractionally integrated approach and implementing cointegration methods that have not yet been used in the study of the Central American Monetary Council. Our results first show that all the series of prices are nonstationary, with orders of integration equal to or higher than 1 in all cases. Looking at long-run equilibrium relationships among the countries, we only found strong evidence of a cointegration relationship in the case of Honduras with El Salvador. All the other vis-a-vis relationships seem to diverge in the long run. Policy implications of the results obtained are also derived in the paper.