Abstract: A wireless telephone system is adapted for serving portable telephone sets of itinerant users. The wireless telephone system is provided with a plurality of radio base stations being organized in at least two groups or paging areas. Each group has a boundary, a portion of each boundary being overlapped by at least one other boundary, and at least two of the at least two groups having at least two radio base stations, one of which is in common with the other group. From time to time in relation to each group, a beacon signal is radio transmitted from a radio base station exclusive to the group for soliciting a recordation response from a portable telephone set of an itinerant user within a beacon zone. When the presence of a respondent portable set is recorded as being within a service area of one of the groups, the portable set is instructed not to respond to subsequent occurrences of the same beacon signal for some hours to avoid cluttering the wireless spectrum with undue supervisory signalling.