Detection of AI-generated content is a crucially important task considering the increasing attention towards AI tools, such as ChatGPT, and the raised concerns with regard to academic integrity. Existing text classification approaches, including neural-network-based and feature-based methods, are mostly tailored for English data, and they are typically limited to a supervised learning setting. Although one-class learning methods are more suitable for classification tasks, their effectiveness in essay detection is still unknown. In this paper, this gap is explored by adopting linguistic features and one-class learning models for AI-generated essay detection. Detection performance of different models is assessed in different settings, where positively labeled data, i.e., AI-generated essays, are unavailable for model training. Results with two datasets containing essays in L2 English and L2 Spanish show that it is feasible to accurately detect AI-generated essays. The analysis reveals which models and which sets of linguistic features are more powerful than others in the detection task.