All three Dutch men’s tennis players are out of the US Open after Botic van de Zandschulp lost his first-round match in straight sets to Holger Rune.

The Dane, seeded 11th, needed two tie-breaks to defeat Van de Zandschulp, who needed a medical time-out in the second set and admitted to being jaded after reaching the final of the Winston-Salem tournament at the weekend.

The 29-year-old Dutchman said he had struggled with the wind on court. “I started getting into the game better, but it took a bit too long for me to get used to it,” he said.

Earlier the Dutch number one, Tallon Griekspoor, seeded 29th for the tournament, succumbed in straight sets to the Frenchman Adrian Mannarino, losing the final set 6-0.

Griekspoor has struggled for form since winning the Mallorca Open at the end of June. He was knocked out in the first round of Wimbledon and has lost his last five singles matches, including a first-round elimination at Winston-Salem, where he was the number 2 seed.

Jesper de Jong, making his US Open debut, went down in five sets to the American Brandon Nakashima, but emerged positive from the defeat.

“I did everything I could and played a really good match,” the 25-year-old told NOS. “If I can reach this level on a daily basis it could be a great year.“

In the women’s draw, Suzan Lamens, the only Dutch player, takes on 18-year-old American Valerie Glozman in her opening round match later on Tuesday.