1. An apparatus for smoothly playing a pre-determined sequence of songs transmitted from a server over the Internet, the apparatus comprising a processor, a first memory that stores at least one program used by said processor to control the playing of the sequence of songs, and a second memory which is available to said at least one program for operations, wherein said at least one program causes said processor at least to: as soon as a song starts to play, start to download, consecutively, a first small portion of each of a number of songs which are, in the pre-determined sequence, subsequent to the song in playing, said downloaded small portions being pre-cached in a buffer which is an area in said second memory; as soon as the user skips to a target song whose first small portion has been pre-cached, start to play the first small portion of said target song; and at the same time start to download the rest of said target song so that as soon as the playing of the first small portion of said target song ends, start to play the rest of said target song which is being downloaded from the server over the Internet.