Argument mining (AM) is the process of automatically extracting arguments, their components and/or relations amongst arguments and components from text. As the number of platforms supporting online debate increases, the need for AM becomes ever more urgent, especially in support of downstream tasks. Relation-based AM (RbAM) is a form of AM focusing on identifying agreement (support) and disagreement (attack) relations amongst arguments. RbAM is a challenging classification task, with existing methods failing to perform satisfactorily. In this paper, we show that general-purpose Large Language Models (LLMs), appropriately primed and prompted, can significantly outperform the best performing (RoBERTa-based) baseline. Specifically, we experiment with two open-source LLMs (Llama-2 and Mistral) with ten datasets.