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Britain’s Amarni Banks fought back to beat former world number 10 Kristina Mladenovic and reach the second round of Wimbledon qualifying.
The 21-year-old harnessed her easy power to beat France’s Mladenovic 4-6 6-4 6-2 at Roehampton.
She will face American 26th seed Kayla Day on Wednesday as she bids to reach a Grand Slam main draw for the first time.
Banks was one of three British women to make it through the first round of qualifying.
Klugman is bidding to reach the main draw of a senior Grand Slam for the first time, having competed in the juniors at Wimbledon last year.
She was impressive against world number 265 Marcinko, who is 358 places above her in the world rankings.
Sonay Kartal was also among the British winners, the 22-year-old coming through 7-6 (8-6) 6-4 against Suzan Lamens of the Netherlands.
Kartal will face China’s Wei Sijia next, while Klugman takes on Czech Linda Fruhvirtova.
American former world number 21 Amanda Anisimova breezed past Greece’s Valentini Grammatikopoulou 6-2 6-3 as she continues her return to the sport.
Players have to win three matches to secure a place in the main draw at Wimbledon, which begins on Monday.
There were eight British women in qualifying action on Tuesday.
Britain’s Emily Appleton was narrowly beaten 3-6 6-3 6-4 by France’s Elsa Jacquemot, while Amelia Rajecki fell 6-4 4-6 6-4 to seventh seed Arina Rodionova of Australia.
Turkey’s Ipek Oz saw off Mingge Xu 6-4 6-4 and Croatia’s Tena Lukas won 6-7 (6-8) 6-4 7-6 (10-8) against Katy Dunne.
Fifteen-year-old British player Mika Stojsavljevic lost 6-3 6-4 to Selena Janicijevic of France.