Abstract In this paper, a continuous time AK model is fully analyzed under the time-to-build assumption. The existence and uniqueness of a (real) balanced growth path as well as oscillatory convergence are proved. Transversality conditions and capital depreciation are highlighted. Moreover, it has been shown how the introduction of the time-to-build assumption supports some interesting empirical evidences such as the negative link between mean output growth and output growth volatility. Finally, numerical simulations are provided for different choices of the time-to-build delay in order to clarify the analytical results.