The paper presents experimental results concerning the comparison of tensile and compressive basic creep behaviours at early ages of two different concretes: a normal strength concrete (NSC) and a very high strength fibre reinforced concrete (HPFRC). This research project has been done in the context of a bilateral collaboration between Polytechnique Montreal and IFSTTAR. Observations on the HPFRC showed specific compressive creep similar to the specific tensile creep. Moreover, the specific creep curves obtained under compressive and tensile loading had always positive values, i.e. they were in same direction of the applied load on specimens. Measurements made on the NSC revealed specific compressive creep with positive values (in the loading direction). However, specific tensile creep presented negative values (opposite direction of loading) for a long period. A physical explanation based on the existence of two mechanisms with opposite effect is proposed to describe these basic creep results. The first mechanism is a coupling between the microcracking process and the water transfers that lead to additional self-drying shrinkage; the second mechanism is the self-healing of concrete induced by the microcracking.