Ropes made of twisted polyester (PET) yarns have been replacing traditional steel ropes and chains as mooring lines for offshore platforms in deep-sea environments. In order to optimise rope manufacture and the design of mooring systems, a thorough understanding of the material's mechanical behaviour is necessary. Besides PET, other materials can also be considered such as PEN, as it also a polyester similar to PET but stiffer. This paper presents a study and comparison of PET and PEN fibres' mechanical behaviour, based on experiments carried out on single filaments. Both fibres show similar non-linear tensile behaviour, with an evolution of modulus in four steps. The same microstructural model is proposed for both fibres, based on microfibrils aligned along the fibre axis and composed of an alternation of amorphous, mesamorphous and crystalline phases. The shape of the tensile loading curve is explained by the successive loading of these phases. Creep behaviour is also evaluated by considering the evolution of creep rate with applied load. This evolution is again similar for PET and PEN, both from a qualitative and quantitative point of view. The similarity in creep rate values for both fibres indicates that the microstructural mechanisms involved in creep may differ from those involved in short term tension loading.