If they do, they'll achieve milestone victories.
Djokovic, trying to complete a career Grand Slam and win his fourth consecutive major title, can become the seventh man with at least 50 match wins at Roland Garros. The others - Nadal, Roger Federer, Guillermo Vilas, Ivan Lendl, Andre Agassi and Nicola Pietrangeli - all won at least one title at the clay-court tournament.
The top-seeded Djokovic enters Thursday's match against 161st-ranked qualifier Steve Darcis of Belgium with a 49-11 record at the French Open. Darcis, meanwhile, is 4-7 in Paris.
''I wish the draw had been different,'' said Darcis, whose most significant victory is beating Nadal at Wimbledon in 2013. ''But ... that's why I play tennis; that's why I started tennis. Playing the No. 1 will be just a great experience. ... Hey, you never know.''
They've played each other twice before - on clay in Rome in 2008, and on a hard court in Miami last year - and Djokovic won all four sets in those matches, two by 6-0.
So Darcis figures he won't be surprised by anything he sees from Djokovic this time.
''I know where I'm going,'' Darcis said, ''but it's still complicated.''
The fourth-seeded Nadal, who owns a record nine French Open championships and 14 major titles in all, can become the eighth man with 200 Grand Slam match wins.
He enters Thursday's match against 99th-ranked Facundo Bagnis of Argentina with a 199-30 mark at the majors. Bagnis, meanwhile, is 2-3.
Here's a look at what else is happening at the French Open on Thursday:
WILLIAMS TIMES TWO: Both Williams sisters are in action, one right after the other, on Court Suzanne Lenglen. First Serena Williams, who is seeded No. 1, faces Teliana Pereira, a Brazilian ranked 81st who never has made it to the third round at a Grand Slam tournament. Williams, in contrast, is seeking her 22nd Grand Slam title, which would equal Steffi Graf for the most in the Open era. Then her older sister Venus, who is seeded No. 9, takes on 20-year-old American qualifier Louisa Chirico, who is ranked 78th. Chirico made it to the semifinals on clay at Madrid this month. ''She's been playing well, right? I haven't seen her play. I don't really know much about her,'' said Venus, who has won seven Grand Slam titles. ''But of course I'm happy to see her doing well. It's always not as much fun when you have to meet an American early on, but the best part is an American will go through.''
TUNISIA'S JAZIRI: No. 7 Tomas Berdych of the Czech Republic plays 72nd-ranked Malek Jaziri, who is trying to become the first man from Tunisia to reach the third round at the French Open since Mustafa Belkhodjia in 1963.
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