This study aims to enhance the automatic identification and classification of metadiscourse markers in English texts, evaluating various large language models for the purpose. Metadiscourse is a commonly used rhetorical strategy in both written and spoken language to guide addressees through discourse. Due to its linguistic complexity and dependency on the context, automated metadiscourse classification is challenging. With a hypothesis that LLMs may handle complicated tasks more effectively than supervised machine learning approaches, we tune and evaluate seven encoder language models on the task using a dataset totalling 575,541 tokens and annotated with 24 labels. The results show a clear improvement over supervised machine learning approaches as well as an untuned Llama3.3-70B-Instruct baseline, with XLNet-large achieving an accuracy and F1-score of 0.91 and 0.93, respectively. However, four less frequent categories record F-scores below 0.5, highlighting the need for more balanced data representation.