Many studies in the empirical literature show that public debt is negatively correlated with economic growth but there is no paper that studies the causal links between these variables using rigorous tests based on Granger's ideas. Accordingly, we investigate the causal links between debt-to-GDP ratio and economic growth using both linear parametric and nonlinear nonparametric Granger causality tests. We focus on 12 euro countries for the period 1970-2012. Our empirical results suggest a unidirectional causality running from debt to economic growth for Spain and Portugal and a bidirectional causality for Belgium, Germany, Greece, Ireland and Italy. No causality in either direction is identified for Austria, Finland, Luxembourg and the Netherlands. Finally, for France, the tests provide evidence for a unidirectional causality running from GDP growth to debt-to-GDP ratio. In addition, the nonlinear tests indicate that overlooking nonlinearities may result in misleading conclusions about Granger causality. Caveats of the analysis, as well as policy conclusions, are also discussed.