The early stages of localised corrosion affecting magnesium(Mg) surfaces when immersed in aqueous sodium chloride (NaCl) solutions involves the propagation of dark regions, within which both anodic metal dissolution and cathodic hydrogen evolution occur. For nominally “pure” Mg, these dark areas can either take the form of discs which expand radially with time, or filiform-like tracks which lengthen with time. For Mg surfaces which display disc-form corrosion features in concentrated NaCl electrolyte, a transition to filiform corrosion (FFC) is observed as the concentration is decreased, indicating ohmic constraints on radial propagation. A similar effect is observed when Mg specimens of different iron impurity are immersed in a fixed, high concentration NaCl solution, where disc-form corrosion is observed on samples having $280 ppm Fe, but FFC predominates at #80 ppm Fe. An in situ scanning vibrating electrode technique (SVET) is used to determine current density distributions within the propagating corrosion features. Cathodic current density values of between 100 and 150 A m2 measured in central areas of disc-like features are sufficient to sustain the radial growth of a local anode at the perimeter of the discs. However, for high purity Mg specimens (#80 ppm Fe), cathodic current densities of 10 A m2 or less are measured over FFC affected regions, indicating that linear propagation arises when there is insufficient cathodic current produced on the corroded surface to sustain radial growth. The results are consistent with surface control of localised corrosion propagation in concentrated electrolyte, but ohmic control in dilute, lower conductivity NaCl solution.