Davydenko won last month's Shanghai Masters
Nikolay Davydenko stayed on target for a place in the ATP World Tour Finals after he beat Alejandro Falla 6-2 6-1 in round one of the Valencia Open.
A title for the Russian second seed would go a long way to securing one of two remaining spots in London at the end of this month.
Top seed Andy Murray, who has been sidelined for six weeks, plays Spaniard Daniel Gimeno-Traver on Tuesday.
Roger Federer beat Olivier Rochus in round one of the Swiss Indoors.
Frenchmen Gilles Simon and Gael Monfils and Spain's Tommy Robredo are also in action in Spain on Tuesday, with all three still in with a slim chance of securing a place in London between 22-29 November.
World number one Federer eased through to the second round of the Davidoff Swiss Indoors in front of a partisan support in his home town of Basle.
The 28-year-old number one seed defeated Belgian qualifier Rochus 6-3 6-4 without offering an opportunity for a break of serve.
Federer was making his 10th appearance in the event, and his first start since mid-September when Switzerland beat Italy in the Davis Cup.
His serve faltered on one occasion, with a single double fault in the opening set, but he fired 12 aces in the match to cruise to victory and set up a second-round clash with Andreas Seppi of Italy.
"I was eager to come out and play again," Federer said.
"It's especially nice to come back on tour with my home tournament where I have so many memories."