The invention relates to a method for storing and passing on multimedia messages for a multimedia call in a packet-switching telecommunication network (TN), with the called subscriber (B subscriber) having network access with a known and predetermined bandwidth to the telecommunication network (TN). In the situation where it is found (1) during the setting up of a multimedia call that the available bandwidth is too narrow (2, 3) because the called subscriber (B subscriber) is currently using a further multimedia service, the multimedia call is diverted (4) to a recording device (ABZ) which is available in the telecommunication network (TN).; A calling subscriber (A subscriber) can then leave a multimedia message on the recording device (ABZ), which is then passed (5) to a local recording device (ABL) for the called subscriber (B subscriber) via the network access and using the bandwidth that is still available. The arrival of the new multimedia message is then indicated (6) to the called subscriber (B subscriber) after complete transmission. The method according to the invention results in the subscriber (B subscriber) in a packet-switching telecommunication network (TN) being informed (6) that a multimedia call has arrived, with the recording device (ABZ) that is available in the telecommunication network (TN) advantageously carrying out a form of buffer function. This buffer function makes it possible to use time expansion to make use of the bandwidth that is still available for transmission of the multimedia message (5).