The aim of the invention is to reduce the time required for transmitting a multimedia message from any sender to any addressee and thus generally cut the cost of the multimedia message service (MMS). Said aim is achieved by keeping a traffic channel connection (NKV) to a receiving telecommunication device (ETKG), which is established by a multimedia message service center (MMNDZ) that has received a multimedia message (MMN) designated by a transmitting telecommunication device (STKG) for said receiving telecommunication device (ETKG), for example, in order to transmit an information message (MN) to the receiving telecommunication device (ETKG) during an SMS session (IS) by means of which the multimedia message service center (MMNDZ) informs the receiving telecommunication device (ETKG) about the arrival of the multimedia message (MMN), established for at least the period of time it takes the receiving telecommunication device (ETKG) to evaluate the received information message (MN) and hold an MMS session (AS) for fetching the message content of the multimedia message (MMN) designated for the receiving telecommunication device (ETKG) from the multimedia message service center (MMNDZ).