The top 60 riders from a field of 75 in today's one-round class progress to tomorrow's second phase, when the race for Team medals also begins.
Madden, Olympic individual bronze medallist four years ago, was eliminated aboard Via Volo, while 2011 World Cup winner Ahlmann clocked up 15 faults on Codex One.
And Switzerland's former world number one Pius Schwizer only just made it, filling the final 60th qualifying place.
'I am hugely disappointed - I can't explain what happened,' Ahlmann said.
Great Britain's riders made a solid start, but it was a disappointing day for Peter Charles.
Former European champion Charles exited the Individual competition on Vindicat. However, his team-mates Ben Maher, Scott Brash and Nick Skelton all enjoyed a trouble-free opening day.
Charles and Vindicat got it all wrong at an early double, knocking down both elements and then collecting two time penalties.
'It was a disastrous start to the round,' Charles said. 'He was a bit tense, he didn't want to take the bridle, so I ended up taking eight strides before fence three when I had planned to go on seven strides.
'I have got to use all my experience to work around it now.'
Team medals will be decided after round two of the competition on Monday, with the Individual medal race reaching its conclusion next Wednesday.
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