The stabilisation of pitch fibres (PFs) is the most important step for their subsequent use in the preparation of carbon fibres (CFs) and their resulting characteristics. The present work studies the influence that the stabilisation time has on the porosity of the CFs, and on the subsequent properties as carbon molecular sieve (CMS). The increase of the stabilisation time carried out at 573 K, from 2 to 8 h favours their CMS properties producing a decrease in the microposity accessible to N2, which gets completely blocked after 6 and 8 h, while the narrow microporosity (V-DR CO2) remains accessible. Adsorption kinetic studies with CH4 and CO2 were performed to assess the possibility of using these CFs as CMS by comparing them with Takeda 3A CMS. The results suggest that there is an optimal stabilisation time which allows the preparation of CFs from an abundant raw precursor with properties similar to Takeda 3A CMS.