In the present research, the uniaxial compression behaviour of concrete under different strain rates is investigated. The investigation emphasises the influence of the strain rate on the development of inelastic deformations due to nonlinear creep for high levels of stress (larger than 70% of uniaxial strength). A clear and consistent decrease of the concrete strength for lower strain rates is observed. Acoustic emission measurements clearly confirm the relationship of this phenomenon to the development of concrete micro-cracking with time. An accurate analytical prediction of the strength and remaining deformation capacity has been obtained by applying the affinity hypothesis and the nonlinear creep coefficient previously developed by the authors for constant loading cases.