Fog disrupted the program at the Sochi Games for the second straight day. The biathlon race had originally been scheduled for Sunday night but now officials hope to start the competition on Tuesday at 2:30 p.m. local time (5:30 a.m. ET).
The snowboard cross was rescheduled for 10:30 a.m. (1:30 a.m. ET) Tuesday.
The International Biathlon Union said this was the first time an Olympic race in that sport had been postponed since 1988 in Nagano, Japan.
Ole Einar Bjorndalen won that race and he is still competing, hoping to win a record 13th Olympic medal when the event is finally contested. Bjorndalen has 13 Olympic medals in his career, tying him for the all-time record with Norwegian cross-country skier Bjorn Daehlie.
Bjorndalen, 40, won the first biathlon event of these Games, the sprint, but failed to medal in his next two races.
Martin Fourcade of France will be trying for his third gold medal of the 2014 Olympics when the race is finally held.
At the snowboarding venue, officials not only postponed the race until Tuesday but also shortened it by eliminating the seeding runs.
All 39 competitors will be in the first round of competition. Groups of contestants ride down a course in which hazards and jumps are encountered and only the top three from each heat advance to the next round. Six snowboarders eventually take part in the finals.
Organizers at first eliminated the seeding round Monday in hopes the fog would lift and the event could be held. A postponement was finally announced.