Magnesium is an excellent candidate as lightweight structural material, but has strong plastic anisotropy, and the activation of, operation of, and competition between different slip and twinning systems remain active areas of research. Here, the nucleation of twinning and basal slip in Mg single-crystalline nanopillars are studied using molecular dynamics over a range of strain rates allowing for reasonable extrapolation to experimental rates. Deformation along the [0 0 0 1] direction shows tension and compression twinning at stresses predicted to be similar to 1400 and similar to 1700 MPa at a strain rate of 10(-3) s(-1). Moreover, twin nuclei are shown to be absolutely stable only above 1170 MPa. No evidence of nanotwinning is found and the twin-growth velocities are very fast (similar to 400 m s(-1)). These results do not support recently proposed mechanisms for nanotwinning. Deformation along the [0 1 (1) over bar 1] direction shows basal dislocation nucleation at stresses of 1000-1300 MPa in tension and 670-900 MPa in compression, at experimental strain rates, with one EAM potential exhibiting compression/tension asymmetry. Size effects are observed between pillars of diameters between 5 and 10 nm, which are attributable to surface stress effects driving nucleation and expected to be irrelevant at experimental pillar sizes (200 nm and above). Overall, most of the observed deformation mechanisms mirror those found in experiments but the stress levels, even when extrapolated to experimental strain rates, remain well above those found in micro-and nanopillar experiments. This indicates that deformation in the experimental specimens is controlled by the motion of pre-existing dislocations or is associated with significant stress concentrations due to surface defects.