The German bid from Munich was due to make the first presentation to the International Olympic Committee on Wednesday, followed by Annecy, France, and Pyeongchang, South Korea.
After close defeats for the 2010 and 2014 Games, Pyeongchang is the early favorite. Munich, hoping to become the first city to host both a Summer and Winter Olympics, is the main challenger. Annecy is the outsider.
Each city had 45 minutes to present its case, followed by 15 minutes for questions and answers.
The IOC will vote later in the day by secret ballot, with the winner expected to be announced by IOC President Jacques Rogge after 11 a.m. EDT.
With seven members absent, 95 IOC members will be eligible to vote in the first round. A majority is required for victory, meaning 48 votes would be enough to win.
If no majority is reached in the opening round, the city with the fewest votes is eliminated and the two remaining cities will go to a second and final ballot.
There has been speculation of a possible first-round win for Pyeongchang, which led in each of the first rounds in the votes for the 2010 and 2014 games but lost in the final rounds to Vancouver and Sochi.
The wild-card could be how many sympathy votes Annecy receives in the first round.
All three cities brought out heavy hitters for the final presentation.
Pyeongchang's delegation includes South Korean President Lee Myung-bak and reigning Olympic figure skating champion Kim Yu-na.
The Munich bid, chaired by two-time Olympic figure skating gold medalist Katarina Witt, has German President Christian Wulff and World Cup football great Franz Beckenbauer. French Prime Minister Francois Fillon is part of the Annecy delegation.
The IOC's trend in recent votes has been to move the games to new frontiers, taking the Winter Games to Russia (Sochi) for the first time in 2014 and giving South America its first Olympics with the 2016 Summer Games in Rio de Janeiro.
The Winter Games have been staged twice in Asia, both times in Japan — Sapporo in 1972 and Nagano in 1998. Pyeongchang, whose slogan is "New Frontiers," says it can spread the Olympics to a lucrative new market in Asia and become a hub for winter sports in the region.
Munich counters that the games need to go back to their spiritual home in Europe and to a country with a history and tradition of winter sports and big crowds.
It's been nearly 80 years since Germany hosted the Winter Games in Garmisch-Partenkirchen in 1936. Garmisch would stage snow events in 2018, while Munich would use many of the facilities from the 1972 Summer Games for the ice competitions.
The Annecy bid, which got off to a slow start and struggled through budget problems and leadership changes, seeks to distinguish itself from its two rivals by promising a simpler "authentic" games in the heart of the French Alps.
IOC votes for the Winter Games can be especially unpredictable, with many members hailing from countries with little or no winter sports tradition. Outside factors come more into play.
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Stephen Wilson can be reached at http://twitter.com/stevewilsonap