Both of those arrested are from outside the county and the 24-year-old and 37-year-old have been arrested on suspicion of violent disorder.
In addition, Cumbria Constabulary has seized a number of weapons including bats, clubs and bladed articles.
Yesterday, the force implemented new powers after it became aware of people travelling to Appleby to cause trouble.
Chief Superintendent Matt Kennerley said: “Expert officers are actively reviewing CCTV footage with the aim of identifying offenders and making further arrests.
“A number of weapons, including sticks and bats of various types, as well as bladed weapons have also been seized by officers.
“There is no place at Appleby for those who travel here intent on disorder and violence – and that is a message which comes not just from the police but the local, settled community and the overwhelming majority of the Gypsy and Traveller community.”
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