The variation with distance of the values of local magnitude, ML, obtained from strong-motion records at short distances to the sources is examined. The available data seem to indicate a gradual decrease with distance from the fault up to a distance of about 20 km followed by a gradual increase for distances in the range from 20 to 100 km. This type of distance dependence can be predicted on the basis of available correlations of peak Wood-Anderson seismograph response with peak velocity and of peak velocity with distance to the fault and local magnitude obtained from actual Wood-Anderson records. These correlations are employed to obtain an alternative relation between local magnitude, synthesized peak Wood-Anderson response and distance to the fault. The alternative relation which is valid only at short distances to the fault gives good agreement with the available data and seems to indicate a degree of saturation of the Wood-Anderson response at short distances. The average estimates of ML based on this alternative relation for several well-recorded events are similar to those obtained on the basis of Richter's standard definition. The alternative estimates have the advantage of removing the distance dependence exhibited by the standard estimates. The effects that this modification of the relation between local magnitude, peak Wood-Anderson response, and distance has on certain estimates of peak strong-motion amplitudes are also examined.