TwistedBolt,
If caverens developed beneath the surface of Mars and gases built upwithin these caverns  then underground rivers would be possible. Dr Warren Nokleberg once said there is no such thing as an underground river but although he is one of the most brilliant men I have ever met, I have always disagreed with his generality.)

Surely ground water exists on Mars as it does here . the overburden wold provide the necessary pressure. I wouldn't be expecting above-ground  rivers on Mars, however  Outside of an occasional gullywasher that carries it's own temporary atnosphere along with it perhaps powered by (are you ready for this - I'm gonna name something after Vile again)  "Vile's Geiser".

BTW sorry for the crossthread
-TJ