However, it's important to note that:
* "Saber-toothed tiger" is a misleading term. While they were large cats with saber-like teeth, they were not closely related to modern tigers.
* Several different species of saber-toothed cats existed. While Smilodon is the most famous, others like Homotherium and Machairodus also lived during the Pleistocene. Their exact time periods varied slightly.
* Their extinction was gradual. Different species of saber-toothed cats disappeared at different points in time. The last known Smilodon species died out around 10,000 years ago in North and South America.
So, while the Pleistocene epoch is the general timeframe for the saber-toothed cats, the exact time period depends on the specific species you're interested in.