Aaron Cook and Lutalo Muhammad both suffered early exits in the World Taekwondo Grand Prix Final in Mexico.
Cook suffered a 10-7 defeat to Argentinian Olympic champion Sebastian Crismanich in the -80kg category.
Then Muhammad also lost, 20-10 against Iranian Mehdi Khodabakhshi.
Olympic -57kg gold medallist Jade Jones will try to do better when she fights on Thursday. Great Britain's Mahama Cho will also aim to win a £3,825 first prize in the +80kg division.