The event, held every May and October, attracts hundreds of visitors
A third person is being sought in connection with a stabbing at the historic Stow Fair in Gloucestershire.
Two people were arrested after a man, 33, was stabbed in the stomach at the horse trading event on Thursday.
A woman, 51, and a man, 58, were remanded in custody by Stroud magistrates on charges of conspiracy to commit grievous bodily harm.
Officers have appealed to a man, believed to be involved in the incident to come forward.
Ch Supt Gary Thompson said police were disappointed that a stabbing occurred at what had otherwise been a low crime event.
The only other incident was the arrest of four people suspected of money laundering.
"We hope that this fact goes some way to giving residents in Stow and those who visit the fair confidence that crime at the event remains incredibly low and any fears that crime increases during the fair are unfounded," said Ch Supt Thompson.
The bi-annual event attracts thousands of Gypsies, travellers and visitors each May and October.
Police had stepped up patrols in response to complaints from some residents about noise, nuisance and litter.
Cotswold District Councillor Barry Gibbs said: "The crime figures - indeed, the lack of them - speak for themselves and bode well for the future."