The first avalanche hit on Sunday after 11:30am (1030 GMT) in the central Switzerland's Bernese Alps, killing a skier, they said. Emergency services were searching for survivors when another struck half an hour later.
Eight helicopters carrying doctors, rescuers and avalanche dogs were despatched to the disaster site and pulled out eight people alive.
Some of the survivors were in a critical condition and three died later in a hospital, including a doctor who had arrived to treat people following the first avalanche.
Rescuers also found the body of a hiker buried in the snow while three other people were reported missing, police from the canton of Bern said in a statement.
In Switzerland's western canton of Valais, a mountain guide and his client were hit by an avalanche at around 2:00pm on Sunday, officials said.
The guide was able to get out alive but his client was killed, the body found buried under 80cm of snow.
The Swiss Institute for Snow and Avalanche Research said there remained "considerable avalanche danger" in much of the Swiss Alps Monday although the risk was forecast to be lower on Tuesday and Wednesday.
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