PARIS - Novak Djokovic insists he isn't keeping tabs on his unbeaten run, which reached 38-0 this season - and 40 consecutive victories dating to December - thanks to a 6-2, 6-1, 6-3 win over Thiemo de Bakker in the first round of the French Open on Monday.

"I'm not counting," the second-seeded Djokovic said with a smile. "I'm not trying to think about the streak that I have."

Others certainly are thinking about it. Indeed, it's the talk of the year's second Grand Slam tournament. Straight-set victories at Roland Garros by other top players such as Roger Federer, top-seeded Caroline Wozniacki, or defending champion Francesca Schiavone - and even 2010 semifinalist Tomas Berdych's surprising five-set loss to a French qualifier - didn't merit as much attention as Djokovic did.

The Serb, who won his second Australian Open title in January, is closing in on the Open-era record for best start to a tennis season by a man: John McEnroe's 42-0 in 1984.

But Djokovic's pals on tour aren't exactly making a big deal about it at the moment.

"In the beginning - I know him very well - I'd kind of joke, 'Hey, let someone else win.' ... Now you almost stay away. It's almost like a pitcher going for a no-hitter," said No. 10 Mardy Fish, who beat Ricardo Mello, 6-2, 6-7 (11), 6-2, 6-4.

Wins over Rafael Nadal - who begins his bid for a record-tying sixth title at Roland Garros on Tuesday - on clay at Madrid and Rome this month have many believing Djokovic could become the first man to win the Australian Open and French Open in the same year since Jim Courier in 1992.

In the second round, Djokovic will meet 60th-ranked Victor Hanescu. Win that, and Djokovic could take on 25th-seeded Juan Martin del Potro. The 2009 U.S. Open champion hasn't been the same player since right wrist surgery last year, but the Argentine got past 6-foot-10 Ivo Karlovic, 6-7 (7), 6-3, 7-5, 6-4.

Down the line, Djokovic's semifinal opponent could be Federer, who completed his career Grand Slam by winning the 2009 French Open, part of his 16 major titles overall.

"Roger can beat anybody if he plays good," was the assessment offered by Feliciano Lopez, the Spaniard who never managed to earn a single break point and lost to Federer, 6-3, 6-4, 7-6 (3).

The man who upset Federer at Wimbledon en route to last year's final, the sixth-seeded Berdych, exited quickly, blowing a two-set-to-none lead, then later wasting a match point, in a 3-6, 3-6, 6-2, 6-2, 9-7 loss to 140th-ranked Stephane Robert.

Two other seeded men lost: No. 22 Michael Llodra and No. 26 Milos Raonic.

Llodra left on an ugly note, likening the atmosphere at his court to an Arab marketplace after receiving a warning from Moroccan chair umpire Mohamed El Jennati for throwing a ball at a female security guard in the stands.

TV footage showed Llodra telling El Jennati: "We are not in a souk. We are not selling carpets in a market."

On the women's side, the top-ranked Wozniacki dominated 40-year-old Kimiko Date-Krumm, 6-0, 6-2, and the fifth-seeded Schiavone beat Melanie Oudin, 6-2, 6-0.

Wozniacki, unbothered by her bandaged left thigh, won the first seven games until Date-Krumm, who made her debut at Roland Garros in 1989 - a year before Wozniacki was born - was able to hold serve.

Wozniacki will next face Aleksandra Wozniak, who beat Junri Namigata, 6-1, 6-1.