FIELD: message delivery through telephone networks. SUBSTANCE: method includes following stages: (a) subscriber A shapes message addressed to subscriber B; mentioned message is stored in memory device 14 of telephone network 10 for the time being; (b) attempt is made to deliver stored message to subscriber B; (c) acknowledgement of message delivery result is passed to subscriber A upon delivery attempts. In order to facilitate acknowledgement procedure for subscriber at the same time minimizing network loading specific information is maintained for subscriber in network concerning availability of delivery acknowledgement services for subscriber that will ensure dispatching specific messages; with delivery acknowledged, acknowledgement of message delivery addressed to subscriber A may be routed to mentioned message delivery services basing on mentioned information, if necessary. EFFECT: facilitated procedure, enhanced reliability of message delivery. 10 cl, 7 dwg
