Theory: It has been argued that because researchers have not taken into account the long-memoried natures of certain political processes - especially the fact that some political time series appear to contain unit roots - some users of level Vector Autoregressions may have reached erroneous conclusions about the validity of important causal relationships and model specifications. Hypothesis: For the first time, this argument is evaluated. The difficulties associated with modeling long-memoried political processes are reviewed. Then several approaches to dealing with them are discussed. One of the most promising approaches, Fully-Modified Vector Autoregression (FM-VAR) is studied in detail. Method: The usefulness of FM-VAR is evaluated in a stylized Monte Carlo investigation and in reanalyses of major existing studies in political science - reanalyses that are representative of the ways in which level-VARs are employed in our discipline. Results: Our experiments indicate that FM-VAR performs well (particularly in terms of size) in small and large samples, in fully and near-integrated systems, and in stationary systems. Most important, use of FM-VAR calls into question some of the major causal findings and specification test results in published studies. The implication, therefore, is that taking into account the trend properties of political processes is essential in theory building in political science.