The first time, eco-activists threw orange confetti and jigsaw pieces on Court 18, and one of them sat on the ground during a match between Grigor Dimitrov and Sho Shimabukuro.
Play was briefly delayed while marshals picked up the pieces. The crowd booed, before security officials removed the protesters.
The eco group objects to Wimbledon being sponsored by Barclays bank, which it claims has lent £30 billion to oil and gas companies in the past two years. Fossil fuels are a large emitter of greenhouse gases, causing climate change.
The Metropolitan Police said a man and a woman had been taken into custody.
In the second case, play was halted, again on Court 18, when another protester, who like the earlier ones was in a Just Stop Oil T-shirt, threw confetti on the grass, interrupting British number one Katie Boulter’s first-round match. He was led off the court.
A man in this case was also arrested on suspicion of aggravated trespass and criminal damage.
Both Boulter and opponent Daria Saville helped clear the court after the protester was escorted away.
The Metropolitan Police said: “We are aware of an incident on Court 18 whereby one male has unlawfully entered the field of play and discharged items onto the playing surface.
“He was immediately removed from the grounds and arrested on suspicion of aggravated trespass and criminal damage.
“The male is now in custody. Play on the court has been temporarily paused while the items are removed and will resume shortly.
“Police and AELTC (All England Lawn Tennis and Croquet Club) Security Teams are responding immediately to deal with these incidents.”
Just Stop Oil said: “We can’t leave it to the next generation to pick up the pieces.”
Earlier, activists in the Harrods department store in Knightsbridge, central London, held placards on an escalator, before security guards bundled a photographer out of the building, Just Stop Oil said.
The protest happened as home secretary Suella Braverman and culture secretary Lucy Frazer held talks with police and sports chiefs on how to prevent Just Stop Oil activists targeting flagship events.
England cricketer Johnny Bairstow carried one demonstrator off the pitch during disruption of the second Ashes Test at Lord’s, following protest action at the rugby final at Twickenham and the World Snooker Championship.
Security had been tightened up at the tennis championships in an attempt to avoid protests.
Deborah Wilde, 68, a retired teacher from London, ran on the court shortly after 2.10pm.
She said: “I’m just an ordinary grandmother in resistance to this government’s policy of serving us new oil and gas licences. In normal circumstances this sort of disruption would be entirely unacceptable, but these aren’t normal circumstances.
“We’ve just had the hottest June on record, breaking the previous record by nearly a whole degree. We don’t need Hawk-eye to see that our government issuing over 100 new fossil fuel licences is a very bad line-call.”
Wimbledon officials said two people had been removed from the grounds and arrested.
Ms Wilde said: “Forget strawberries and cream – scientists are warning of impending food shortages, mass displacement and war.
“We are facing new pandemics, economic inflation and increasingly authoritarian governments who will attempt to crush civil unrest.
“This is a crisis and it needs a crisis response. I want a safe future, not just for my grandchildren but for all children around the world and the generations to come.”
The Met Office confirmed on Monday that June was the hottest on record.
Several slow marches were held on Wednesday in central London, including in Hammersmith, Victoria, Westminster, Kensington, Tower Bridge and Parliament Square.
Just Stop Oil protester Simon Milner-Edwards, 66, a retired musician, from Manchester, who was part of the first Wimbledon court invasion, said: “I’m not prepared to let our politicians wreck everything and leave the next generation to pick up the pieces.
“The last thing I want to do is spoil people’s enjoyment of Wimbledon, but right now, on Centre Court, it’s humanity versus oil and gas - and the umpire is getting every call wrong.”
She said she would continue to work with the Home Office and sporting bodies “to ensure this small minority do not ruin our summer of sport”.
Ms Frazer said it was “really disappointing to see yet more disruption of our world-class sporting events”.
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