This thesis presents the first results for the Automated Essay Scoring (AES) task on the ASK corpus of Norwegian learner language. It explores a wide variety of classifier architectures, including linear models, simple neural networks (MLPs) and more specialized neural architectures, namely convolutional and recurrent neural networks. Furthermore, it explores training an AES model using multi-task learning, with Native Language Identification (NLI) as an auxiliary task. Three different formulations of the AES task are explored: nominal classification, regression and ordinal regression. A number of model hyperparameters are investigated, such as the performance of attention-based architectures compared to simpler pooling methods: mean-over-time and max-over-time.