The Voyager-1 probe may be outside the Solar System, some scientists say.
If confirmed, it would be the first man-made object to exit.
Launched in September 1977, the probe was sent initially to study the outer planets, but then just kept on going.
Researchers studying its data say the craft appears now to be in a realm of space beyond the influence of our Sun.
But Nasa says that it regards Voyager as still being inside the Solar System.
The probe is currently moving more than 18 billion km from Earth, or 123 times the distance between our planet and the Sun.