Two young farmers were arrested during the annual convention in Blackpool, police said.
The force said the majority of the 6,000-strong crowd were 'well behaved and enjoyed the weekend without causing any trouble', echoing the comments of the weekend's organisers.
But, in a statement, it said: "Unfortunately a minority got carried away and behaved in a way which was unacceptable.
"We received several complaints of anti-social behaviour and made two arrests: One on suspicion of assault, and another for criminal damage.
"We also responded to a further complaint of assault, which was dealt with between the two parties involved.
"We want all visitors to Blackpool to have a good time. However, when that behaviour becomes antisocial or criminal, we will take action against those responsible."
Yesterday, The Gazette revealed how the future of the weekend event, which was held at the Winter Gardens, was under threat because of the 'appalling' behaviour of some young farmers, who were caught on film attacking a motorist, lying in front of traffic, climbing street signs, and chanting expletives.