This invention is especially intended for playing Ring Tones (referred to hereinbelow as "RT's") on a called computer terminal, and/or Ring Back Tones (referred to hereinbelow as "RBT's") on the calling computer terminal, in voice communications selected from users of different computer terminals, mainly personal computers (referred to hereinbelow as "PC's") by means of a network which is at least partially a data network capable of supporting voice, such as the Internet. RT's and/or RBT's are played by means of a continuous download of said tones (referred to hereinbelow as "streaming") given that neither RT nor RBT are present at any time on any of the PC's, but rather are downloaded from a remote server where RT's and/or RBT's are located. In general, the user of the called PC will be the one determining what RT and/or RBT will be played in terms of the different optional factors such as which calling PC is involved.