Serena Williams began her campaign to return to world number one at the Qatar Open by beating Russian Daria Gavrilova while Maria Sharapova, among the American's rivals for top spot, also progressed on Tuesday.
Second-seed Williams, who will reclaim the number one position if she reaches the semi-finals, enjoyed a 6-2 6-1 second-round win against the 160th-ranked Gavrilova.
The 15-times grand slam winner has not topped the rankings since October 2010, but is close to returning to the pinnacle having claimed last year's Wimbledon and U.S. Open titles.
Williams, who has now won 57 of her last 60 matches, broke Gavrilova in the sixth game of the first set and then raced away with the match in 54 minutes.
Question marks hung over the world number two's fitness heading into the event after she lost in the Australian Open quarter-final last month while suffering with back and ankle injuries.
"Mostly I've just been trying to play smoothly and avoid problems, and just do the things I've been working on," Williams said on the WTA website (www.wtatennis.com).
"Physically I'm feeling better, and hopefully I can stay on that level. Let's go onto the next round now."
Third-ranked Sharapova broke serve in the first game against France's Caroline Garcia before cruising to a 6-3 6-2 win in one hour and 16 minutes.
It was a rematch of their tussle at the French Open two years ago when the Russian found herself 6-3 4-1 down before rallying for a three-set victory.
"I had a really tough match against her in our previous encounter, so I really wanted to start better this time, as opposed to the way I started against her last time," Sharapova said.
"I think she's an up-and-comer who is still making that transition from the juniors to the pros. It's one of the toughest things getting your feet on the ground with the game itself but I think we will be seeing her for many more years."
French Open champion Sharapova also has a slim chance of returning to the top spot but needs to win the tournament and hope Williams falls short of the last four and current world number one Victoria Azarenka fails to reach the final.
Belarussian Azarenka gets her campaign underway with a second round match against Romina Oprandi on Wednesday.
(Writing by Toby Davis in London; editing by Ken Ferris)