We explore the capability of four open-sourcelarge language models (LLMs) in argumentation mining (AM). We conduct experiments on three different corpora; persuasive essays(PE), argumentative microtexts (AMT) Part 1 and Part 2, based on two argumentation mining sub-tasks: (i) argumentative discourse units classifications (ADUC), and (ii) argumentative relation classification (ARC). This work aims to assess the argumentation capability of open-source LLMs, including Mistral 7B, Mixtral8x7B, LlamA2 7B and LlamA3 8B in both, zero-shot and few-shot scenarios. Our analysis contributes to further assessing computational argumentation with open-source LLMs in future research efforts.