This paper presents a two period overlapping generations model with endogenous growth in the presence of a public sector with objectives of convergence for public debt and primary balance to GDP ratios. In order to ensure the existence of converging paths towards the target values of fiscal variables, we introduce a simple fiscal policy rule. According to this rule, the primary balance ratio is adjusted in function of the distance between the current and the target levels of the public debt and the primary surplus to GDP ratios. It is shown that the fiscal rule displaying time invariant parameters may produce non linear dynamic processes of adjustment of the fiscal ratios as well as endogenous fluctuations in the rate of growth of the economy. In addition the transitional process towards fiscal targets critically depends on the adjustment tool chosen by the fiscal authorities to implement the rule.