Summary: We introduce the intensity-based defaultable Lévy Libor model, which generalizes the default-free Lévy Libor model introduced by E. Eberlein and F. Özkan [Math. Finance 13, No. 2, 277–300 (2003; Zbl 1049.91066)], and the intensity-based defaultable model presented by T. R.Bielecki and M.Rutkowski [Credit risk: modeling, valuation and hedging. Berlin: Springer (2002; Zbl 0979.91050)] by embedding it in the defaultable HJM framework introduced by Eberlein and Özkan [loc. cit.]. We also derive some additional results for defaultable HJM models such as the dynamics of credit spreads. We then go on and model the default-free Libor rates and credit spreads as the primal variable and derive the dynamics of the defaultable Libor rates under the defaultable forward measure. Finally, we derive an explicit formula for options on credit default swaps, using an idea introduced by S. Raible [Lévy Processes in finance: Theory, numerics and empirical facts, PhD thesis, University of Freiburg i. Brsg. (2000; Zbl 0966.60044)].