The Port Lympne reserve is an animal and safari park that also serves as a breeding sanctuary for rare and endangered animals.
The spokesperson said: “Late in the afternoon on Saturday, two cobes escaped from their enclosure and managed to access a public path.
“After concerted attempts to return the animals to their enclosure, it was felt that as a Category 1 animal they could become a danger to the public and the decision to euthanize them was made.
“All necessary authorities have been kept fully informed and an internal investigation will take place in due course.”
In April, it was revealed that five animals escaped their enclosures in as many months in 2020.
A park inspection report, obtained through an access to information request, indicated that two female deer pigs escaped after a fence broke on March 5. One was injured and the other was shot.
A South American jungle cat left its enclosure last May after getting out, while a rust-spotted cat from India did not return to its enclosure after going missing last July through a hole made by a rat.
On August 9, a bear escaped and was coaxed with food. He escaped to an area that is not accessible to the public. A gate to the enclosure had been left open by a guard who was then sanctioned.
There were other animal escapes and guards were also killed. In February 2000, Darren Cockrill, 27, a guard, was killed by an elephant in the park.
The zoo has insisted it operates with high standards of animal care despite escapes and deaths.
Earlier this year, the Charity Commission launched a statutory inquiry into the Aspinall Foundation to investigate “serious concerns” regarding its governance and financial management.
The regulator said it began reviewing the charity in July 2020 amid “concerns about handling conflicts of interest and related party transactions.”
A spokesperson for the charity said at the time: “Our directors will continue to work in an open and transparent manner with the Charity Commission to ensure governance and best practice compliance.”
Ms Johnson previously worked as the Conservative Party’s communications chief and for Oceana, a marine conservation charity.