Serena Williams began her campaign to return to world tennis number one at the Qatar Open by beating Russian Daria Gavrilova while Maria Sharapova, among the American's rivals for top spot, also progressed.
Second-seed Williams, who will reclaim the number one position if she reaches the semi-finals, enjoyed a straight sets 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 US Open titles.
Williams has now won 57 of her last 60 matches.
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.
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 Thursday.