A transient analysis of an SEM experiment is given with the purpose of determining directly the lifetime of minority carriers in a semiconductor material. The injection takes place below a surface normal to the junction and expressions are derived for the current-decay which ensues when the electron beam is cut off. The decay of the current is shown to be overall different from a purely exponential one. Indeed, the results, which are given for zero and infinite surface-recombination velocity, vs, show a time-lag in the current-decay, which increases with the distance of the beam from the junction. Even in its final stages the decay fails to be purely exponential. It is shown that serious errors in the evaluation of lifetime may occur if the true nature of the decay is not taken into account.