However organisers, who have been forced to cancel the opening races on Saturday and Sunday because of strong winds and persistent snowfall, are hopeful the men's super-G can still be held Monday.
Strong winds at the top of both super-G runs are set to abate, and temperatures are due to drop ahead of Monday's scheduled start of 1130 GMT.
If Monday's race is cancelled organisers will aim to hold both races on Tuesday.
Atle Skårdal, the chief race organiser on the World Cup series, reported: "I think it is realistic to have a men's super-G tomorrow (Monday). We're starting to see better conditions coming up."
North-westerly winds coming via Norway have caused havoc, and organisers have been praying for drier easterly winds to blow over from Russia.
A drop in temperatures, predicted for Tuesday, would also help in bringing an end to the snowfall and hardening the snow which has already fallen on the runs.
Skårdal said Sunday's conditions meant there was no chance the women's race could be held.
"The conditions simply did not comply with the requirements we need to hold a super-G race at the world championships," he said.
"There were still very strong winds at the top (of the run). We also had a lot of snow, which needed to be cleaned off the piste.
"And the lower part of the course, where the temperatures were three degrees (celsius) warmer, is still wet – and that poses safety issues for various reasons.
"The jury was unanimous in coming to the decision to cancel the race."
It could not be a worse start to the championships for the hosts, who are holding the competition for the first time since 1954.
But a wide range of off-piste activities – such as concerts and shows – have not been affected, meaning the thousands of spectators who have travelled to the resort have been kept entertained.
The fact the super-G races have been pushed back means the scheduled three downhill training runs for the men and the women will have to be reduced to two.
International SKi Federation (FIS) general secretary Sarah Lewis insisted the postponements did not pose a major threat to the staging of other races in the competition.
"Obviously there are concerns for a lot of the parties involved but at this stage we're not concerned about not being able to hold the other events," she said.
"We still have reserve days this week, and also next week if it comes to that."
Skårdal added: "If we cannot hold the men's race on Monday, then we will look to hold both super-G races on the Tuesday, the men at 1030 (0930 GMT) and the women at 1230 (1130) GMT."