The first victim fell on Wee Binnian mountain just before midday and the second man fell about an hour later while walking on Slieve Commedagh.
The police and other emergency services were called to both incidents but the men were pronounced dead at the scene.
A third man fell in the Mournes at about 2.30pm but he was rescued and sustained a suspected broken ankle.
Inspector Frances McCullough said: "Police and other emergency services responded but unfortunately both men died at the scene."
Earlier on Sunday, police had urged members of the public to "exercise extreme caution due to strong winds" in the area.
More to follow…
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