Summary: Modelling patterns in credit risk using survival analysis techniques have received considerable and increasing attention over the past decade. In these models, the predictor of the hazard of default is often expressed as a simple linear combination of the risk factors. In this work, we discuss how these models can be enhanced using generalised additive models (GAMs). In the GAMs framework, the predictor is formulated as a combination of flexible univariate functions of the risk factors. In this paper, we parametrise GAMs for credit risk data in terms of penalised splines, outline the implementation via frequentist and Bayesian MCMC methods, apply them to a large portfolio of credit card accounts, and show how GAMs can be used to improve not only the application, behavioural and macro-economic components of survival models for credit risk data at individual account level, but also the accuracy of predictions. From a practitioner point of view, this work highlights that some accounts may actually become more (less) attractive to the lender if flexible smooth functions are used whereas the same applicant may be denied (accepted) a loan if the linearity assumption is forced.