For the purpose of extending the usefulness of a Geiger counter to higher radiation intensities, it has been suggested that the voltage applied to its electrodes be a periodically repeated pulse rather than the usual dc. If the duration of the pulse is of the order of the spread time of the discharge in the tube, the output currentvsradiation intensity relation will differ from the usual linear one, largely because the resulting current surge may not reach its maximum before the end of the applied pulse. This relation will therefore depend, among other factors, on the not fully understood mechanism by which the discharge spreads. Using probability considerations, we here calculate this relation as a function of the response of the tube under ordinary operation. If the discharge spreads rapidly (e.g., exponentially) initially, an approximate general relationship not involving the detailed spread mechanism may be established. The response to be expected in two types of tubes is discussed in detail, using models for the spread mechanism which are mathematically simplified though probably physically adequate.