In this article, we develop an endogenous growth model to analyze the relation between tax evasion and public debt accumulation. Our results are threefold. First, our model exhibits a multiplicity of equilibria in the long run: there is a low-growth and high public debt balanced growth path (BGP) and a high-growth and low-public debt BGP. Second, we show the existence of threshold effects in the tax evasion-public debt nexus. In low-growth economies, tax evasion negatively affects public debt while the relation between the two variables is characterized by a U-shaped curve in high-growth economies. Finally, regarding the local stability of the BGPs, we show that the high BGP is always well-determined. However, the topological behavior of the low BGP is more complex: it can either be locally determined, undetermined or overdetermined. In the latter case, a Hopf bifurcation appears depending on the level of tax evasion.