Abstract. Empirical investigations about rating transitions show typically a non-Markovian behavior. We take this as a motivation to generalize existing models and determine conditions for absence of arbitrage in a general forward rate model. We allow for compensator of default times with singular components which generalizes the so-called intensity based framework. The results are the starting point for explicit modeling approaches and we propose a extended affine model for this and discuss open questions. This is joint work with J. Jakubowski and M. Nieweglowski.