While training in the forest, Gluteus Maximus encounters Asterix and Obelix, who unintentionally outdo him at running, then javelin and boxing, thanks to the power of the magic potion.

The entire (male) population of the village travels to Olympia in Greece (aboard a galley where they have to do the rowing), where Asterix and Obelix register as athletes (with Getafix as their coach) and the others all enjoy a holiday.

Alarmed, the Greeks send a judge to warn the Romans that even if they think drinking will somehow make them better athletes, it will be held against them as all artificial stimulants are forbidden, prompting Veriambitius to tell him about the Gauls' magic potion.

After the announcement, Asterix and Getafix start talking, very loudly, about a cauldron of magic potion left in an unguarded shed.

The race begins, and the Roman athletes easily beat Asterix - they all overtake him and cross the finish line simultaneously.

Gluteus' apparent victory is shown to have greatly pleased Julius Caesar, who promotes Maximus to centurion and Veriambitius to tribune.

There is also another subplot about Julius Caesar's son Brutus, who also wants to marry the princess, overthrow his father and take over the Roman empire.