Switzerland's Didier Cuche came third in the men's downhill in Beaver Creek in the United States on Friday, ahead of fellow countryman Didier Defago, who was fourth.
The race was won by Austria's Michael Walchhofer who clocked 1min 13.74sec, edging American Nyman into second at 0.05sec.
Cuche, who was fastest in both training and the downhill portion of Thursday's super-combi, was 0.10 off the winning pace. He made two mistakes in quick succession early, largely because he came into the upper section with less speed than in training due to the lowered start.
"That's where I lost the victory," said Cuche after earning the 32nd podium of his career. "Sometimes you win and are surprised, but today I was skiing for the victory. So I'm happy I'm on the podium but a bit disappointed with the mistake I made," he said.
Cuche, who leads the World Cup downhill standings, also reached the podium in second place in a Super G last Sunday at Lake Louise, Canada.
The race was contested in cold and windy conditions on the 2,122-metre Birds of Prey course where Norway's Aksel Lund Svindal, the reigning overall World Cup champion, crashed during training in midweek, sidelining him for the races.
Walchhofer's triumph ended a slump for the Austrian men, who had failed to win a World Cup race this season.
"It was an important victory for me," said Walchhofer, who has finished second, third, fourth, fifth and sixth in Beaver Creek over the past five years. "It's one of the most difficult downhills."
It was his 12th career World Cup victory and ninth in the downhill. Nyman made a mistake on the lower half of the course that cost him the victory, and the American had to settle for second.
A Super-G event is scheduled in Beaver Creek on Saturday with a giant slalom race contested on Sunday.
swissinfo with agencies
Beaver Creek, United States – World Cup downhill
1. Michael Walchhofer, Austria, 1 minute, 13.74 seconds.
2. Steven Nyman, United States, 1:13.79.
3. Didier Cuche, Switzerland, 1:13.84.
4. Didier Defago, Switzerland, 1:13.93.
5. Marco Buechel, Liechtenstein, 1:13.94.
6. Bode Miller, United States, 1:14.10.
7. Peter Fill, Italy, 1:14.12.
8. Mario Scheiber, Austria, 1:14.13.
9. Kurt Sulzenbacher, Italy, 1:14.27.
10. Andrew Weibrecht, United States, 1:14.28.