In the 19th century there was controversy over whether horses, when galloping, ever got all four feet off the ground. One of the first time-lapse photographers proved they did. (Foregoing based on aging memory).
I was reminded of that when I saw the pictures of a bear chasing a bison down a road, CNN via Treehugger.
When you're running for your life, or for your dinner, you get all four feet off the ground.