In this paper we propose to analyze the dynamic of the relation between public debt and economic growth rate for Euro area countries by employing a wavelet approach, establishing thus both short-term and long-term correlations between these two variables. In this way we will present time-frequency dependencies between debt and economic growth and differentiate between short term and long-term effects. High levels of public debt have a negative impact on the economic output, because they entail concerns about debt sustainability. Non-linear analysis of the debt-growth nexus shows the existence of thresholds from which rising indebtedness can hamper economic growth. Using wavelet analysis, we demonstrate that there is a strong relation between public debt and economic growth, especially for high frequencies, public debt having a significant impact on economic growth in case of periods situated above 2 years for most Euro Zone member states.