Writer identification is the task of determining the author of a sample handwriting from a set of writers. In this paper, we propose Gaussian Mixture Models (GMMs) to address the task of off-line, text independent writer identification of text lines. The resulting system is compared to a system that uses a Hidden Markov Model (HMM) based approach. While the GMM based system is conceptually much simpler and faster to train than the HMM based system, it achieves a significantly higher writer identification rate of 98.46% on a data set of 4,103 text lines coming from 100 writers.