In this paper we present first results for the task of Automated Essay Scoring for Norwegian learner language. We analyze a number of properties of this task experimentally and assess (i) the formulation of the task as either regression or classification, (ii) the use of various non-neural and neural machine learning architectures with various types of input representations, and (iii) applying multi-task learning for joint prediction of essay scoring and native language identification. We find that a GRU-based attention model trained in a single-task setting performs best at the AES task.