Log-linear models have recently been used in acoustic modeling for speech recognition systems. This has been motivated by competitive results compared to systems based on Gaussian models, and a more direct parametrisation of the posterior model. To competitively use log-linear models for speech recognition, important methods, such as speaker adaptation, have to be reformulated in a log-linear framework. In this work, an approach to log-linear affine feature transforms for speaker adaptation is described. Experiments for both supervised and unsupervised adaptation are presented, showing improvements over a maximum likelihood baseline in the form of feature space maximum likelihood linear regression for the case of supervised adaptation.