World number one Djokovic, the 2011 champion, beat Germany´s Florian Mayer 6-3, 7-5, 6-4, in the Serb´s first grass-court outing of the season and his first match since his shattering five-set semi-final loss to Nadal at the French Open.[break]
"It was a big pleasure to play in front of a packed Centre Court against a tricky rival like Mayer. He´s got a great variety of shots and his game is well-suited to grass," said Djokovic, who next faces Bobby Reynolds of the United States.
Defending champion Williams, chasing a sixth Wimbledon title and 17th major, racked-up her 32nd successive win, cruising to a 6-1, 6-3 win over Luxembourg´s Mandy Minella.
Her 57-minute romp on Centre Court briefly deflected attention away from the storm surrounding her controversial comments on a US high school rape case and the fall-out from her criticism of Maria Sharapova´s love life.
The 31-year-old took out her frustrations on the hapless Minella, the world number 92 who has never defeated a top-30 player let alone one of Williams´s calibre whose French Open title three weeks ago took her majors haul to 16.
Victory was also her 75th in her last 78 matches, a run that stretches back to her shock first round departure at Roland Garros in 2012, the worst Grand Slam exit of her career.
Tuesday´s 32nd successive win took her to within just three of the record set by older sister Venus in 2000.
"I never think about the run, I just treat every match like a new one," said Williams.
"It was special coming out as defending champion. I played great and I have some great memories."
Williams did not concede a single point on her serve in the first set and finished the match with 25 winners to Minella´s five.
She goes on to face French qualifier Caroline Garcia, who she beat in the second round in Paris, for a place in the last 32.
Russia´s Maria Kirilenko, who made the quarter-finals last year, slumped to a first round exit at the hands of Britain´s world number 38, Laura Robson, who claimed a 6-3, 6-4 win.
"That was a big one for me just because of all the nerves and playing in front of your home crowd at Wimbledon," said Robson, a former junior champion.
On a bad day for Russians, 21st seeded Anastasia Pavlyuchenkova slumped to a 6-0, 6-1 loss to Bulgaria´s Tsvetana Pironkova who made the semi-finals in 2010.
Russian 13th seed Nadia Petrova went out 6-3, 6-2 to Karolina Pliskova of the Czech Republic.
Kimiko Date-Krumm, just three months shy of her 43rd birthday, made the second round with a 6-0, 6-2 win over Carina Witthoeft, an 18-year-old German qualifier, who was just four when the Japanese star made her Wimbledon debut in 1989.
"I´m taking care of my body, because of course the most difficult thing is recovery. I need more training. But if I do too much I feel tired," said Date-Krumm, a semi-finalist in 1996.
"I like Chinese tea. Sometimes Japanese tea. I drink a lot. I have a tea pot I always I carry. It´s here with me now."
Li Na, the Chinese sixth seed, enjoyed a comprehensive 6-1, 6-1 defeat of Dutchwoman Michaella Krajicek.
The 31-year-old former French Open champion next faces Romania´s Simona Halep.
"It was a pretty good start to Wimbledon. Because the last two years I didn´t do well on the grass court," said Li, twice a quarter-finalist.
"I have to get used to playing on the grass. I was feeling pretty happy."
Polish fourth seed Agnieszka Radwanska enjoyed a 6-1, 6-1 win over Austrian qualifier Yvonne Meusberger.
Radwanska, the runner-up to Williams last year, next faces Mathilde Johansson of France.
In the men´s first round, Spanish fourth seed David Ferrer beat Argentina´s Martín Alund 6-1, 4-6, 7-5, 6-2.
Bulgarian 29th seed Grigor Dimitrov, the man at the centre of the Williams-Sharapova spat, cruised past Italy´s Simone Bolelli, 6-1, 6-4, 6-3.
Argentinian eighth seed Juan Martin del Potro, who missed the French Open through illness, saw off Spain´s Albert Ramos 6-2, 7-5, 6-1.
Australia´s Bernard Tomic put out American 21st seed Sam Querrey, 7-6 (8/6), 7-6 (7/3), 3-6, 2-6, 6-3.
Tomic, a quarter-finalist in 2011, was playing without his controversial father in the crowd.
John Tomic, who is facing a criminal charge in Spain for assaulting his son´s hitting partner, has been banned from the club by Wimbledon authorities.
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