[2] The club is most famous for being the winners of the first edition of the Coupe Van der Straeten Ponthoz in 1900, one of the world's first international footballing competitions, in which it played and defeated the reigning champions of Belgium, Switzerland and the Netherlands on three successive days.

The team managed to win the Netherlands Football League Championship five times (all of which in the 19th century), including three titles in a row between 1897 and 1899, going undefeated in the latter season (1898–99).

On the following day, in the semi-finals, RAP beat the champions of Switzerland, Grasshopper Club, again by the minimum margin of 3–2, with Jan van den Berg netting two of Amsterdam's goals.

[7] In the first half, HVV proved their favoritism by going ahead thanks to an own goal from RAP's goalkeeper, Koopman (sometimes credited to Beukema), but the Amsterdammers fought back and found an equalizer with 10 minutes to go, courtesy of van den Berg.

Their victory in the final meant that in a space of three days, RAP played and defeated the reigning champions of Belgium, Switzerland, and the Netherlands.

Thus, RAP might be considered the first ever continental European Champions,[3] although this title is also contested by Vienna Cricket and Football-Club, who were the winners of the first Challenge Cup in 1897, a competition between clubs in Austria-Hungary.

Volharding (Dutch for Perseverance), which is the other old Amsterdam football club, found themselves in a similar predicament, always merely one or two points above RAP in the table, but still considered classified in the same section.